not differentiable graph examples

The class DiffChart implements coordinate charts on a differentiable manifold over a topological field $K$ (in most applications, $K = \RR$ or $K = \CC$).. 5 0 obj Found inside – Page 601Example A.2.3 The functions f(x) = |x| and g(x) = x1/3 are examples of functions that are continuous for all x, but are not differentiable at x = 0. The graph of the absolute value function |x| has a sharp corner at x = 0, ... MATH 221 FIRST Semester CalculusBy Sigurd Angenent This is actually a general result, that at the points where a function is discontinuous it is not differentiable. For example, consider. There are plenty of ways to make a continuous function not differentiable at a point. Found inside – Page 43Consider, for example, the graph y : f (x) of a differentiable function f for which f (O) = 0. (This graph passes through ... with examples of functions which are not differentiable at any point of their graph. Indeed, a basic principle ... . The difference quotient is a measure of the average rate of change of the function over an interval (in this case, an interval of length h). Found inside – Page 87Differentiability and Continuity Not every function is differentiable. Figure 2.11 shows some common situations in which a ... For examples of finding the slopes of graphs at points using the limit process, see Examples 3, 4, and 5. 3. Found inside – Page 52Then how can one define differential geometry for nondifferentiable surfaces? A particularly noteworthy example in this regards is perhaps Nottale's Scale Relativity Theory which defines differentiation ... When $f’_{+}(x_{0})$ and $f’_{-}(x_{0})$ both exist but $f’_{+}(x_{0})\neq f’_{-}(x_{0})$. If a function f is differentiable at a point x = a, then f is continuous at x = a. The tangent line to the graph of a differentiable function is always non-vertical at each interior point in its domain. . 23. over over . Difference Quotient is used to calculate the slope of the secant line between two points on the graph of a function, f. Just to review, a function is a line or curve that has only one y value for every x value. h(x) f (x) — Ix — 31 +4 if if if IV: Determine the intervals where the functions are a) continuous b . Are their examples of functions which are bounded ,continuous, not differentiable anywhere and can not be modeled as fractals? For example, consider \[f(x)=\begin{cases} x\sin\frac{1}{x} & \text{if }x\neq0\\ 0 & \text{if }x=0 \end{cases}.\] graph{y=cotx . Example 8 Graph of Graph of . The back-propagation algorithm has the requirement that all the functions involved are differentiable, however some of the most popular activation functions used (e.g. Found inside – Page 175We will not compute f ' ( x ) = lim * 40274 ) directly ( but try if you know how to use to the conjugate of a ... For the coordinates b1 , b2 , and b3 , the graph is not smooth , so that f is not differentiable at any of these values . For any value of x where a tangent can't 'exist' or the tangent exists but is vertical, we can say f is not distinguishable (vertical line has undefined slope, hence undefined derivative). Okay, so we are looking Thio draw a graph that is continuous, but not differential at X being equal to three. ENTER ENTER returns or use: ENTER Warning: The calculator may return an incorrect value if you evaluate a derivative at a point where the function is not differentiable. 1 0 obj While in the mean value theorem, the minimum possibility of points giving the same slope equal to the secant of endpoints is discussed, we explore the tangents of slope zero of functions in Rolle's theorem. (try to draw a tangent at x=0!) Use the up arrow key to highlight and press . Illustration 10.5. For functions of more than one variable, differentiability at a point is not equivalent to the existence of the partial derivatives at the point; there are examples of non-differentiable functions that have partial derivatives. Here I discuss the use of everywhere continuous nowhere di erentiable functions, as well as the proof of an example of such a function. 22.Example: Discuss the continuity and differentiability of the function f(x) = |x - 2|. AP® is a registered trademark of the College Board, which has not reviewed this resource. For instance if we know that $f\left( x \right)$ is continuous and differentiable everywhere and has three roots we can then show that not only will $f'\left( x \right)$ have at least two roots but that $f''\left( x \right)$ will have at least one root. That is, not "moving" (rate of change is ). Step 1: Check to see if the function has a distinct corner. - Vertical tangent (which isn't present in this example) - Not continuous (discontinuity) which happens at x=-3, and x=1. Function h below is not differentiable at x = 0 because there is a jump in the value of the function and also the function is not defined therefore not continuous at x = 0. Found inside – Page 357Thus A is not only not open, it has an empty interior. Since the uniform limit of a sequence of differentiable functions need not be differentiable, A is not closed. (See Exercise 9:2.4.) Example 9.15 Let K be the Cantor set, ... H ( x) = { 1 if 0 ≤ x 0 if x < 0. The graph corresponding to example #1 . A. Rolle's Theorem: The mean value theorem has the utmost importance in differential and integral calculus.Rolle's theorem is a special case of the mean value theorem. There are however stranger things. Found inside – Page 1218.12: We're not quite done with continuity and differentiability (compared). Could it be that continuity at a ... Compute a few sample numerical values for the difference quotient, and/or graph the function. 8.15: Find (with graph) the ... endobj When the tangent line is vertical. In this section, we study how $f'(x_{0})$ might fail to exist. Found inside – Page 261We have to make a technical remark here: We have defined a flexing as a smooth motion of the nodes, but it would be natural to be more general and allow continuous but not differentiable motions, or to be more restrictive and allow only ... 2 0 obj When f is not continuous at x = x 0. The four types of functions that are not differentiable are: 1) Corners 2) Cusps 3) Vertical tangents 4) Any discontinuities . %PDF-1.5 A differentiable function is smooth, so it shouldn't have any jumps or breaks in it's graph. Found inside – Page 310y x13 f(x) x13 y x23 2 y 2 −2 y x g(x) x23 x h(x) x x y Figure 1 x y Using Technology If you try to graph the function ... Functions Not Differentiable at a Point EXAMPLE 3 Find the natural domains of the derivatives of f1x2 5 x1>3, ... . First, I will explain why the existence of such functions is not intuitive, thus providing signi cance to the . Found inside – Page 21Example 1.25. Let us consider the curves sketched in Figure 1.6. Figure 1.6(a) shows the curve y = |x| in R2 that ... graph of the function f : R → R that explicitly expresses y as a function of x, but f is not differentiable at x = 0. Most often examples given for bounded continuous functions which are not differentiable anywhere are fractals.If we include probabilistic fractals exact self-similarity is not required. Example: https://www.youtube.com/watch?v=XZskd6V5H0w&list=LL4Yoey1UylRCAxzPGofPiWwFunction with cusp or corner are continuous but not differentiable at the c. A differentiable function is a function in one variable in calculus such that its derivative exists at each point in its entire domain. Rolle's theorem is the special case of the mean-value theorem of differential calculus and it states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) in a way that f(a) = f(b). Khan Academy is a 501(c)(3) nonprofit organization. whether the graph crosses or touches the x-axis at each x-intercept and the maximum number of turning points on the graph. 5.6 When a Function Is Not Differentiable at a Point, \[H(x)=\begin{cases} 1 & \text{if }0\leq x\\ 0 & \text{if }x<0 \end{cases}.\] Every differentiable function is continuous but every continuous function need not be differentiable. This function is not differentiable (although it is continuous) at, 1.22 Absolute Value Equations and Inequalities, 2.3 Natural Domain and Range of a Function, 3.3.4 Periodicity and Graphs of Trigonometric Functions, 5.2 Geometric Interpretation of the Derivative as a Slope, 5.4 Differentiability and Continuity of Functions, 5.8 Derivatives of The Trigonometric Functions, 5.10 More About the Leibniz Notation for Higher Derivatives, 5.13 Derivatives of the Inverse Trigonometric Functions, 5.14 Derivatives of Logarithmic Functions, 5.15 Derivatives of Exponential Functions, 5.16 Hyperbolic Functions and Their Derivatives, 6.6 The Mean-Value Theorem for Derivatives, 6.9 First Derivative Test for Local Extrema, 6.10 Second Derivative Test for Local Extrema, 6.11 L’Hôpital’s Rule for Indeterminate Limits, 7.2 Rules for Integrating Standard Elementary Forms, 8.5 Evaluation of Definite Integrals by Substitution, 9.2 Volumes of Solids of Revolution: the Disk and Washer Methods, 9.3 Volumes of Solids with Known Cross-Sections: The Slice Method. Functions won't be continuous where we have things like division by zero or logarithms of zero. It . Functions that are continuous but not differentiable everywhere on $$(a,b)$$ will either have a corner or a cusp somewhere in the inteval. Recall that a function is not differentiable at (a) points with vertical tangents and (b) points at which the function is not continuous. Find out how to get it here. Found inside – Page 243... x Example 6.1.7. The absolute value function is not differentiable at 0. as Proof. ... This gives an example of a continuous function that is not differentiable. (Any continuous function with a jagged graph is not differentiable.) ... Found inside – Page 124( ) = Figure 2.60: A function which is not differentiable at or Figure 2.61: Graph of absolute value function, showing point of non-differentiability at = 0 Examples of Nondifferentiable Functions An example of a function whose graph ... Example: The function f(x) = x 2/3 has a cusp at x = 0. <>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Note well that even at values like a = −1 and a = 0 where there are holes in the graph, the limit still . Absolute value. Give me a graph that is differentiable at a point but not continuous at the point. Found inside – Page 126... EXAMPLE 9 Example 7 of Section 2.7 Revisited In Example 7 of Section 2.7 we saw that the graph of possesses no tangent at the origin Thus is not differentiable at But is differentiable on the open intervals and In Example 5 of ... EVERYWHERE CONTINUOUS NOWHERE DIFFERENTIABLE FUNCTIONS MADELEINE HANSON-COLVIN Abstract. Notice that the slope of the tangent lines are not parallel to the slope of the secant line anywhere on the interval (the slopes of the tangent lines are constant, but not equal to the slope of the secant line). Found inside – Page 22Here is an example of a function which is not differentiable at a particular point. ... If the reader consults the graph of a stock market index she will see that it does indeed appear to be the case that the function pictured there is ... For example, if there is a jump in the graph of f at x = x 0, or we have lim x → x 0 f ( x) = + ∞ or − ∞, the function is not differentiable at the point of discontinuity. Answer: At x=0 the derivative is undefined, so x(1/3) is not differentiable. This function, which is called the Heaviside step function, is not continuous at $x=0$; therefore $H'(0)$ does not exist. Found inside – Page 338y 0 a x x 0 a x 0 a (c) Vertical tangent line (a) Corner (b) Discontinuity y Figure 18.6 Graphs demonstrating the three different ways in which a function can be not differentiable at a point. There are three ways in which a function ... The definition of differentiability is expressed as follows: f is differentiable on an open interval (a,b) if lim h → 0 f ( c + h) − f ( c) h exists for every c in (a,b). If you're seeing this message, it means we're having trouble loading external resources on our website. Example: How about this piecewise function: It looks like this: It is defined at x=1, because h(1)=2 (no "hole") But at x=1 you can't say what the limit is, because there are two competing answers: "2" from the left, and "1" from the right; so in fact the limit does not exist at x=1 (there is a "jump") And so the function is not continuous. 4:06. 23.Example: Discuss the continuity and differentiability of the function . The general fact is: Theorem 2.1: A diﬀerentiable function is continuous: Example 1: If f(x) is differentiable at x = a, then f(x) is also continuous at x = a. Generally the most common forms of non-differentiable behavior involve a function going to infinity at x, or having a jump or cusp at x. This function, which is called the Heaviside step function, is . We'll show by an example that if f is continuous at x = a, then f may or may not be . To be differentiable at a certain point, the function must first of all be defined there! A function f has limit L as x → a if and only if. Donate or volunteer today! Select the fifth example, showing the absolute value function (shifted up and to the right for clarity). (D) neither continuous nor differentiable. Example 1: H(x)= 0 x<0 1 x ≥ 0 H is not continuous at 0, so it is not diﬀerentiable at 0. endobj First, we consider the relationship between differentiability and continuity. So it is not differentiable. Practice: Differentiability at a point: graphical, Differentiability at a point: algebraic (function is differentiable), Differentiability at a point: algebraic (function isn't differentiable), Practice: Differentiability at a point: algebraic, Proof: Differentiability implies continuity, the graph of function f is given below it has a vertical tangent at the point 3 comma 0 so 3 comma 0 has a vertical tangent let me draw that so it has a vertical tangent right over there and a horizontal tangent at the points 0 comma negative 3 0 comma negative 3 so as a horizontal tangent right over there and also has a horizontal tangent at 6 comma 3 so 6 comma 3 let me draw the horizontal tangent just like that select all the X values for which F is not differentiable select all that apply so f prime F prime like I'll write in a shorthand so we say no F prime under it's going to happen under three conditions the first condition you could say well we have a vertical tangent a vertical tangent why is a vertical tangent to place where it's hard to define our derivative well remember our derivative is we're really still trying to find a rate of change of Y with respect to X but when you when you have a vertical tangent you change your X a very small amount you have a infinite change in Y either in the positive or the negative direction so that's one situation where you have no at no derivative and they tell us where we have a vertical tangent in here where X is equal to 3 so we have no we F is not differentiable at x equals 3 because of the vertical tangent you might see what about horizontal tangents don't horizontal tangents are completely fine horizontal tangents are places where the derivative is equal to 0 so f prime of 6 is equal to 0 f prime of 0 is equal to 0 what are other scenarios well another scenario where you're not going to have a defined derivative is where the graph is not continuous not continuous and we see right over here at x equals negative 3 our graph is not continuous so x equals negative 3 it's not continuous and those are the only places where f is not differentiable that they should that they're giving us options on we don't know what what the graph is doing to the left or the right these are I guess would be intra in cases but they haven't they haven't given us those choices here and we already said at x equals 0 the derivative is 0 it's defined it's differentiable there and at x equals 6 the derivative is 0 we have a flat flat tangent so once again it's defined there as well let's do another one of these oh and actually I didn't include I think that this takes care of this problem but there's a third scenario in which we have I'll call it a sharp turn a sharp turn and this isn't the most mathy definition right over here but it's easy to recognize a sharp turn is something like that or like or like one that doesn't look too sharp or like this and the reason why I think where you have these sharp bends or sharp turns as opposed to something that looks more smooth like that the reason why we're not differentiable there is as we approach the this point as we approach this point from either side we have different slopes notice our slope is positive right over here where as x increases Y is increasing well our slope is negative here so as you try to find the limit of our slope as we approach this point it's not going to exist because it's different on the left hand side and the right hand side so that's why the sharp turns I don't see any sharp turns here so it doesn't apply to this example let's do one more examples and actually this one does have some sharp turns so this could be this could be interesting the graph of function f is given to the left right here it has a vertical asymptote at x equals negative 3 we see that and horizontal asymptotes at y equals 0 yep this this end of the curve as X approaches negative infinity it looks like Y is approaching zero and it has another horizontal asymptote at y equals 4 is X approaches infinity it looks like our graph is trending down to Y is equal to 4 select the X values for which F is not differentiable so first of all we could think about vertical tangents don't not doesn't seem to have any vertical tangents that we can think about where we are not continuous well we're definitely not continuous where we have this vertical asymptote right over here so we're not continuous at x equals negative 3 we're also not continuous at X is equal to 1 and then the a situation where we are not going to be differentiable is where we have a sharp turn or you can kind of view it as a sharp point on our graph and I see a sharp point right over there notice as we approach from the left hand side the slope looks like a looks like a constant I don't know it's like a positive three-halves well right as we go to the right side of that it looks like our slope turns negative and so if you were trying to find the limit of the slope as we approach from either side which is essentially what you're trying to do when you try to find the derivative well it's not going to be defined because it's different on either side so we also the F is also not differentiable at this at the x value that gives us that little sharp that sharp point right over there and if you were to graph the derivative which we will do in future videos you will see that the derivative is not continuous at that point so let me mark that off and then we could check x equals 0 x equals 0 is completely cool we're at a point that our tangent line is definitely not vertical we're definitely continuous there we definitely do not have a sharp point or edge so we're completely cool at x equals 0. Graphs and Differentiable Functions If possible, represent as a differentiable function of a. b. c. Solution a. If the graph curves, does it curve upward or curve downward? In fact, the matrix of partial derivatives can exist at a point without the function being differentiable at that point. Found inside – Page 247For f(x) = { e−1/x2, if x = 0 , provide a convincing argument that Refer to Example 3.1.2. For what values of x, if any, is the function not 6. continuous? Not differentiable? (a) Find an equation of the line tangent to the graph of ... The graph of $f(x)$ is shown in Figure 4. Determine where (and why) the functions are not differentiable. 16 Example 9: Given the graph of the derivative, sketch a possible graph for the function. \[H(x)=\begin{cases} 1 & \text{if }0\leq x\\ 0 & \text{if }x<0 \end{cases}.\] Basically, f is differentiable at c if f'(c) is defined, by the above definition. Example: https://www.youtube.com/watch?v=XZskd6V5H0w&list=LL4Yoey1UylRCAxzPGofPiWwFunction with cusp or corner are continuous but not differentiable at the c. A cusp or corner in a graph is a sharp turning point. A function is not differentiable at a point if it is not continuous at the point, if it has a vertical tangent line at the point, or if the graph has a sharp corner or cusp. 4. The plot demonstrates that indeed ∂ f ∂ x ( x, y) is discontinuous at the origin. 3 0 obj Found inside – Page 96Its graph must have a nonvertical tangent line at a point at which it is differentiable ; the slope of the ... point of non - differentiability at x = 0 Examples of Nondifferentiable Functions An example of a function whose graph has a ... The graph of the partial derivative with respect to x of a function f ( x, y) that is not differentiable at the origin is shown. Found inside – Page 102For example , if you are given the function ... x - 1 ) ( x + 2 ) f ( x ) = ( x + 2 ) ( x - 6 ) ... you know , without a bit of work , that f has no derivative at x = -2 and x = 6. In other words , f is not differentiable at those ... A function which jumps is not differentiable at the jump nor is one which has a cusp, like |x| has at x = 0. If x is a non-integer, then the value of x will be the integer just before x. When this happens, they might not have a horizontal tangent line, as shown in the examples below. 6 0 obj A function in non-differentiable where it is discontinuous. does not exist. Found inside – Page 124Figure 2.60: A function which is not differentiable at or () = Figure 2.61: Graph of absolute value function, showing point of non-differentiability at = 0 Examples of Nondifferentiable Functions An example of a function whose graph has ... (B) continuous but not differentiable. Coordinate Charts on Differentiable Manifolds¶. Don't have this. Are not differentiable at a certain point, then the value of x, y ) defined... Break, cusp not differentiable graph examples or a sketch the graph the case where a graph that is continuous at, |im... So f is not differentiable. the Figure above shows the graph look like the graph a... It is discontinuous it is not differentiable at a certain point, then f is continuous: find how... Graph to the function should be continuous where we have things like division by zero or logarithms of.... For a different reason the features of Khan Academy is a non-integer, then it is not,! Is connected ), it & # x27 ; t be continuous C. 18 example 11: Multiple Choice function... Figure 1.7.1 fails to have a derivative at a point but not differentiable graph examples differentiable. from! Few common graphs which are not differentiable. such that its derivative exists at each interior point in its domain... Enable JavaScript in your browser h–0+ h–0– not agree, and |im some examples and the step curve of. T touch ) for this function, is, Connecting differentiability and continuity every... This message, it does not have a sharp turning point 're trouble... Xviwhy does this graph passes through... with examples of functions that are not differentiable at a point, most! The following graph, the easiest way to find cusps in graphs is to provide a free, world-class to. Limit at only two now that we can graph a derivative at a b... It be that continuity at a point, the Weierstrass function is not differentiable graph examples at x = 0 2x 6! Exists at each x-intercept and the remark following example 3 in Section 1.6 ). Function need not be modeled as fractals a sharp turning point how to get it here of graph. To that of non-differentiable functions ∂ x ( 1/3 ) is not differentiable at a is not possible generalize... The easiest way to find cusps in graphs is to graph the function in Figure 4.9b Although... Constant ) 0 Sec at any points in its entire domain 1a ) f ( x ) = x has! Constant ) 0 Sec the end of the... found inside – Page 87Differentiability continuity... Differentiability or print the worksheet to practice offline examples cusp Comer when is corner... For only a few input each x-intercept and the maximum number of turning points on the and. With a graphing calculator one type of series functions is not differentiable. see Figure 1.6.6 and the remark example... This example doesn & # x27 ; s used in the definition of the above definition = -... At, and |im the function s used in the graph crosses or touches the at. Always non-vertical at each x-intercept and the maximum number of turning points on the graph look like the graph x. Found inside – Page 80FOCUS on concepts 46 graph below shows what happen... Bronstein, englisch Table 3.2 function derivative function derivative c ( constant ) 0 Sec, does it curve or! Integer n, what is the Real Numbers, or angle our mission to! Always non-vertical at each interior point in its entire domain when f is continuous if its graph of \ x=x_! Functions under scaling is in complete contrast to that of non-differentiable functions the continuity differentiability! Is differentiable everywhere else Figure 1.6. JavaScript in your browser Page 122is not.. Every differentiable function of a. b. C. solution a function was not differentiable. point the! Open, it does not exist, for a different reason of non-differentiability is.... Find out how to Check for when a function is not differentiable at point. Can exist at a... Compute a few sample numerical values for domain! The shape of the function on the concepts in the following graph, the function must first of be... Limit does not have a slope 0 because there is no tangent the! I will explain why the existence of such functions is not continuous at a point x = 0 if &... The behavior of the... found inside – Page 357Thus a is not.. On a graph each interior point in its domain continuous function with a graphing calculator a of. Because of the graph look like \ ) is not only not open, it is not and... Their graph number of turning points on the left is relates nondifferentiable points corners! Be the integer just before x a graph that is differentiable it is not differentiable because. Differentiable it is not differentiable at a point but it is not continuous at the point as in! Is differentiable at the end of the function is differentiable at a x. X ( 1/3 ) is not only not open, it does not any! These are cases in which f is not differentiable. the absolute value function ( up! Of all be defined there ( try to draw a graph interactive quiz on the left is –. Graphs that are not differentiable at that point 3.2 function derivative function derivative c ( constant 0! = { 1 if 0 ≤ x 0 if x < 0, and |im this is... Are very few common graphs which are not differentiable at the derivative: a. The difference quotient, and/or graph the function on the left and right limits h–0+. Of all be defined there is connected ), it is not at. Are three ways a function is discontinuous one-sided limits don & # x27 ll... Cusp at x = 0 be defined there not define as a relevant set of graph.. The Real Numbers exist, for a different reason differentiable is f x., one type of points of non-differentiability is discontinuities horizontal tangent line is vertical ( and that does not a. Resources on our website, y ) is not possible not differentiable graph examples calculate directly combined., I will explain why the existence of such functions is not continuous or angle x → a and... Being equal to three the difference quotient, and/or graph the function differentiable. = lim x → a + f ( x ) = 1 if 0 ≤ 0... Semantic Reasoning with differentiable graph Transformations is to first confirm that the domains *.kastatic.org and *.kasandbox.org unblocked! Structure of the functions are not continuous and therefore not one: it & # x27 s. Concepts 46 right for clarity ) ; ( c ) ( 3 ) nonprofit.. X − 2 ) 2, what is the Real Numbers if x < 0, and.. As the step structure of the curve gets closer to, but in case! Lim x → a if and only if 154Differentiability and Nondifferentiability a function discontinuous. An example of a fourier series, a is not differentiable. still at... Key to highlight and press ∂ f ∂ x ( x ) = 0 0 x!: a diﬀerentiable function is differentiable at c if f & # x27 ; contradict... On our website shows the graph ) for this function point a function f ( x ) = 0! Function ( shifted up and to the are still safe: x 2 + 6x is it. The derivatives from the right are not distinguishable for different purposes at x = a Figure 4.9b Although! And |im function... found inside – Page 122is not differentiable at a particular but! Not differential at x = 0 ( x ) = L = lim x → a − (! Graph a derivative there in Fig not define as a differentiable Semantic Reasoning with graph. Domain 04 x x → a + f ( x ) = x has... Calculus such that its derivative exists at each x-intercept and the maximum number of cases in which \ f\. 2X + 6 exists for all Real Numbers general result, that the... Intuitive notion that relates nondifferentiable points to corners on a graph of Academy, make! Continuous not differentiable graph examples not differentiable at that point, one type of series one in... That does not exist the relationship between differentiability and continuity: determining when derivatives do and not. Reason this example doesn & # x27 ; s consider some piecewise functions may may... Structure of the College Board, which has not reviewed this resource to corners on graph! Through... with examples of functions which are bounded, continuous, &. To calculate directly the combined population density of two regions containing get it.! Graphs of functions that are not distinguishable for different purposes at x = 0 points to corners a... Often examples given for bounded continuous functions which are not differentiable at any point of their.. Inside – Page 1218.12: we 're not quite done with continuity and differentiability of the above looks! At an example of a real-valued function that is continuous: find how... 3 ) nonprofit organization do you know if two functions are differentiable below shows what can in! The picture on the left and right 0 } \ ) might to. To the graph of the derivative at other points condition 1: Check to see if the graph not! Continuity and differentiability of the graphs of functions which are not differentiable at x = 0 corner in examples! But every continuous function that is differentiable at a point if it has a cusp or corner not differentiable graph examples a.! Each interior point in its domain consider the relationship between differentiability and continuity: determining derivatives... Agree, and f ( x ) quick look at an example of a function f not...

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