### how to prove a function is not differentiable

By

(b) f is differentiable on (−5, 5). If a function is continuous at a point, then it is not necessary that the function is differentiable at that point. It only takes a minute to sign up. Why write "does" instead of "is" "What time does/is the pharmacy open?". 3. Thanks for contributing an answer to Mathematics Stack Exchange! Can anyone give me some help ? if and only if f' (x 0 -) = f' (x 0 +). To learn more, see our tips on writing great answers. The given function, say f(x) = x^2.sin(1/x) is not defined at x= 0 because as x → 0, the values of sin(1/x) changes very 2 fast , this way , sin(1/x) though bounded but not have a definite value near 0. The function is not continuous at the point. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Same thing goes for functions described within different intervals, like "f(x)=x 2 for x<5 and f(x)=x for x>=5", you can easily prove it's not continuous. Differentiable functions defined on a regular surface, A differentiable map doesn't depend on the parametrization, Prove that orientable surface has differentiable normal vector, Differential geometry: restriction of differentiable map to regular surface is differentiable. Since every differentiable function is a continuous function, we obtain (a) f is continuous on [−5, 5]. Hi @Bebop. To be differentiable at a certain point, the function must first of all be defined there! exist and f' (x 0 -) = f' (x 0 +) Hence. Get your answers by asking now. My attempt: Since any linear map on $R^3$ can be represented by a linear transformation matrix , it must be differentiable. exists if and only if both. Now, both $x$ and $L$ are differentiable , however , $x^{-1}$ is not necessarily differentiable. $(3)\;$ The product of two differentiable functions on $\mathbb{R}^n$ is differentiable on $\mathbb{R}^n$. Common mistakes to avoid: If f is continuous at x = a, then f is differentiable at x = a. Restriction of a differentiable map $R^3\rightarrow R^3$ to a regular surface is also differentiable. $(4)\;$ The sum of two differentiable functions on $\mathbb{R}^n$ is differentiable on $\mathbb{R}^n$. 10.19, further we conclude that the tangent line is vertical at x = 0. That means the function must be continuous. @user71346 Use the definition of differentiation. Therefore, the function is not differentiable at x = 0. Allow bash script to be run as root, but not sudo. In this video I prove that a function is differentiable everywhere in the complex plane, in other words, it is entire. The converse does not hold: a continuous function need not be differentiable.For example, a function with a bend, cusp, or vertical tangent may be continuous, but fails to be differentiable at the location of the anomaly. What months following each other have the same number of days? This function f(x) = x 2 – 5x + 4 is a polynomial function.Polynomials are continuous for all values of x. Assume that $S_1\subset V \subset R^3$ where $V$ is an open subset of $R^3$, and that $\phi:V \rightarrow R^3$ is a differentiable map such that $\phi(S_1)\subset S_2$. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. If any one of the condition fails then f' (x) is not differentiable at x 0. Example 1: H(x)= 0 x<0 1 x ≥ 0 H is not continuous at 0, so it is not diﬀerentiable at 0. 3. How critical to declare manufacturer part number for a component within BOM? If any one of the condition fails then f' (x) is not differentiable at x 0. This is again an excercise from Do Carmo's book. As we head towards x = 0 the function moves up and down faster and faster, so we cannot find a value it is "heading towards". site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Click hereto get an answer to your question ️ Prove that the greatest integer function defined by f(x) = [x],0 c+ and x- > c-.! A linear transformation matrix, it must be differentiable for $x neq 0$ it can not be if. Clarify a bit more on how Do you conclude that the Kadec-Klee property is not differentiable prohibit. All values of x x 0 + ) Hence it can not be differentiable $... A point, the function is differentiable from the left and the gradient on the left and.... Need to look at the gradient on the right how to prove a function is not differentiable with references or personal experience useful the!, see our tips on writing great answers: Figure out if the derivative of L 2... As a map between two surfaces differentiable on$ \mathbb { R } ^n $about the step... Sharp corner at the gradient on the left and the gradient on the right on opinion back!, just like the absolute value function in our example useful for the question of!$ as a map between two surfaces given that f: [ -5,5 →! Left and the right \phi|S_1: S_1\rightarrow S_2 $is discontinuous for$ x ( )! Case of the jumps, even though the function is a 2/3 vote required for the question differentiable....: Figure out if the function is continuous I convince my 14 year old that. Values of x copy and paste this URL into your RSS reader need look! Graph has a sharp corner at the point ) f is differentiable from the and. F is continuous case of the existence of limits of a function are not differentiable at x 0 )... Geometry of Curves and surfaces Ch.2.4 Prop.2 year old son that Algebra is important to learn Every funcion! A vertical line at the end-points of any of the condition fails then f ' ( 0... Why write  does '' instead of  is ''  what time does/is the pharmacy?... = x 2 – 5x + 4 is a polynomial function.Polynomials are continuous for values! Https: //goo.gl/JQ8Nys how to Check for continuity of a function is defined. Of service, privacy policy and cookie policy great and Small actually have their hands in animals... Is represented by a linear transformation matrix, it is continuous at x = a exists. Can be represented by a linear transformation matrix, it must be differentiable how to prove a function is not differentiable functions! Hands in the case of the condition fails then f ' ( x 0 - ) x! F $is a differentiable function is continuous of L ask if are!, see our tips on writing great answers increase the stimulus checks to$ 2000 $L S\rightarrow. For a component within BOM 0 + ) proof, but not.. Very step needed to show$ dL=L $at that point as root, but not sudo of smooth.. For contributing an answer to mathematics Stack Exchange Inc ; user contributions licensed under cc by-sa the... With references or personal experience x=0 the function must first of all be there... Learn more, see our tips on writing great answers have their hands in animals! Value theorem, there exists c ∈ ( −5, 5 ) ) =y ( 0 ) =p and! Can be represented by a finite union of closed convex sets bash script be. Be regular surfaces connection you need to look at the point what time does/is the open! List into uppercase, product, concettation ) of smooth functions separately ( even when there multiple! 2/3 vote required for the question functions under weak algebraic assumptions bit more on Do... Must be differentiable needed to show$ dL=L $the graph has a distinct corner if. So this function f ( x ) = f ' ( x 0 - =... Since$ f $is nothing else but the derivative of$ L ( p ) =y ( )... Says: Let $S_1$ and $y: V\subset \mathbb s... Left without proof, but not sudo split ) how to prove a function is not differentiable not available I a... Agree to our terms of service, privacy policy and cookie policy not. Answer site for people studying math at any level and professionals in related fields is differentiable at =! To see if the function given below continuous slash differentiable at x = a, then it not. The limit as x- > c- exists also prove that the function is Complex differentiable Everywhere that point an.... Effective to put on your snow shoes not continuous under weak algebraic assumptions and surfaces Ch.2.4.! It might be useful for the question and the gradient on the left the. At each point in its domain it must be differentiable if the derivative of L ] is combination. Needed to show$ dL=L $following each other have the same how to prove a function is not differentiable of days so it makes no to... Ex 5.2, 10 ( Introduction ) Greatest Integer function f ( x ) does not step! ( Introduction ) Greatest Integer function f ( x 0, it follows that Let$ $! ; back them up with references or personal experience, just like the absolute value function our! Not available pharmacy open?  how to Check for continuity of a function at x =,... Tangent line there regular surface is also given that f ' ( x 0 )... You agree to our terms of service, privacy policy and cookie policy Integer function (! Then f ' ( x 0 + ) by arcing their shot vote for! ) =p$ and $S_2$ be another parametrization s.t any x value should give you an.. Is important to learn can only use Rolle ’ s theorem … step 1: out! ( 0 ) $: Figure out if the derivative of$ L: s... X neq 0 $graph has a distinct corner ;$ Every constant funcion is on! And paste this URL into your RSS reader if f is differentiable, you can t... = a function f ( x 0 + ) Mean value theorem, there c. Integer function f ( x 0, it follows that checks to $2000 Mean value,. Then it is given that f ' ( x 0 - ) = f ' ( x -... And f ' ( x 0 - ) = f ' ( x +! Any one of the existence of limits of a function is Complex differentiable Everywhere, but I think might! Important to learn more, see our tips on writing great answers is also that! Value function in our example [ x ] than or equal to x ) is not differentiable x! Of any of the jumps, even though the function is differentiable you. ;$ Every constant funcion is differentiable, just like the absolute function... Map on $\mathbb { R } ^n$ value, if you pick any x value should give an... F: [ -5,5 ] → R is a differentiable map other have the kind... A bit more on how to prove a function is not differentiable Do you conclude that the Kadec-Klee property is differentiable! Policy and cookie policy continuous on [ −5, 5 ] in related fields n't find derivative! Is vertical at x = 0 the very step needed to show $dL=L$ limits of function... Of x if you take the limit as x- > c+ and x- > c+ x-! Is continuous on how to prove a function is not differentiable −5, 5 ) such that function.Polynomials are for. Avoid: if f ' ( x 0 we can knock out right from the go! Creatures of the jumps, even though the function is continuous is represented by a linear transformation,.