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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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$x=1$, $x=5$

01:55

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 8

The Derivative as a Function

Limits

Derivatives

Missouri State University

University of Michigan - Ann Arbor

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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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So we're given this graph of this function and were asked where this function F is not differentiable. Okay. So what we can see is that this is a smooth curve all the way through Until we get to x equals four. At which time we have this corner. That happens right? So at x equals four. Yeah. Is not differential. Remember the derivative have prime is the slope of the tangent line at that X. Well, the problem is with this corner here, there is no tangent line there And x equals four. There is no tangent line due to the corner happening the sharp turn until therefore it is not differentiable. At X equals four.

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