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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2.7, Problem 35E

To determine

**To state:** The graph of the function *f* is not differentiable at which the numbers.

Expert Solution

The function *f* is not differentiable at −4 and 0.

**Note:** The function *f* is not differentiable at the point *a*, then it must satisfies any of the following conditions.

(i) The function *f* is discontinuous at the point *a.*

(ii) The function *f* has a corner point at the point *a.*

(iii) The function *f* has a vertical tangent at the point *a.*

From the graph of *f*, it is observed that *f* has a corner point at *f* has no tangent at that point and it is not differentiable at

The graph of *f* has a jump discontinuity at *x* approaches 0.

Therefore, *f* is discontinuous at

Thus, it can be concluded that, *f* is not differentiable at the point