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The graph of $ f $ is given. State, with reasons, the numbers at which $ f $ is $ not $ differentiable.

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02:07

Daniel Jaimes

01:11

Carson Merrill

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 8

The Derivative as a Function

Limits

Derivatives

Sharieleen A.

October 23, 2020

Finally, the answer I needed, thanks Daniel J.

That was not easy, glad this was able to help

Campbell University

Harvey Mudd College

Idaho State University

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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The graph of $ f $ is give…

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$37-40$ The graph of $f$ i…

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Yeah. All right. So the question that I'm looking at has to do with places where functions are not differentiable. Um since there's no like graph um specific to this question provided, I'm just going to spend a little bit of time talking about places you want to look for um when you're looking for uh numbers where functions are not discontinuous. Okay. Or not? Sorry? Differentiable. Alright. So really we're looking for points of discontinuity. Okay. So we're looking for things like holes. Okay. So if I have a graph, here's my ex and my white access X. Y. And maybe my graph looks something like this, but I have one point there. Yeah, that's not. Mhm. That would be a that point right there, wherever whatever X value that is um the function would not be differentiable at that point. Okay. Another one is with vertical assume totes. Yes. The civil service. So if I have, for example, maybe some sort of like, mm hmm. Students, you gotta be like this sense. Mhm. This is something like this. Okay, wherever that vertical ascent, oh, whatever that X value is here, your function would not be just would not be um differentiable at that point. Um The other one that we can talk about is um jump just kind of unease. Okay. So if I have a piece wise function of some sort and maybe my graph goes like this and then jumps, we would not be differentiable at that point. Okay. Um also the other one is at what they call cusp sis. Okay. And a cusp Sorry. They'll expect a cusp is the best example of this is um the absolute value of X. Yes. Okay. So wherever you're v point is whatever your vertex is right there, that point is not going to be differentiable. Okay, So those are kind of the big ones that you want to look for when you're answering answering questions like this. That was helpful. It's.

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