# The numbers at which the function f is not differentiable.

### Single Variable Calculus: Concepts...

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

### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter 2, Problem 39RE
To determine

Expert Solution

## Answer to Problem 39RE

The numbers at which the function f is not differentiable are x=4,1,2,5.

### 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 given graph, it is clearly observed that x=4, 2 are two discontinuous points of f.

Thus, f is not differentiable at x=4, 2.

From the graph of f, it is observed that f has a corner point at x=1. That is, f has no unique tangent at that point and it is not differentiable at x=1.

The graph of f has a vertical tangent at the point x=5. Therefore, by note-(iii), f is not differentiable at the point x=5.

Thus, the numbers at which the function f is not differentiable are x=4,1,2,5.

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