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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2, Problem 14RCC

(a)

To determine

**To describe:** The meaning for *f* to be differentiable at *a.*

Expert Solution

If *a* is appoint in the domain of a function *f,* then *f* is said to be differentiable at *a* if the derivative *f* has non-vertical tangent line at the point *f* is differentiable at a point *a* then *f* must be continuous at *a*.

(b)

To determine

**To describe:** The relation between differentiability and continuity.

Expert Solution

All differentiable functions are continuous, but not all the continuous functions are differentiable.

Let a function

Function

Since, *x* approaches

Take limit as *x* approaches to

Hence

Since there exist *f,*

(c)

To determine

**To sketch:** A function that is continuous but not differentiable at

Expert Solution

**Example:**

Let the function *f* is continuous but it is not differentiable at 2.

**Graph:**