BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2.7, Problem 35E
To determine

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

Expert Solution

Answer to Problem 35E

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

Explanation of Solution

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 x=4. That is, f has no tangent at that point and it is not differentiable at x=4.

The graph of f has a jump discontinuity at x=4. That is, the limit does not exist because the left and right hand limits are not equal as x approaches 0.

Therefore, f is discontinuous at x=4.

Thus, it can be concluded that, f is not differentiable at the point x=0.

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