# The function can fail to be 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 15RCC
To determine

## To describe: The function can fail to be differentiable.

Expert Solution

### Explanation of Solution

The three main ways that the functions to be differentiable are given below:

(i) The function may be discontinuous at a point.

Example: Let the function f(x)=1x.

Graph:

(ii) The function may have a corner at a point.

Example: Let the function f(x)=|x|.

Graph:

(iii) The function may have a vertical tangent at a point.

Example: Let the function f(x)=|x|13|x|x has a vertical tangent line at x=0

Graph:

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