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Calculus: Early Transcendentals | 9th Edition | ISBN: 9781337613927 | Authors: Daniel K. Clegg, Saleem Watson, James Stewart
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?At what numbers is the following function t differentiable? Give a formula for g’ and

Chapter 2, Problem 76

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QUESTION:

At what numbers is the following function t differentiable?

Give a formula for g’ and sketch the graphs of g and g’.

Questions & Answers

QUESTION:

At what numbers is the following function t differentiable?

Give a formula for g’ and sketch the graphs of g and g’.

ANSWER:

Step 1 of 4

Given function is

To find at what numbers the function is differentiable.

Clearly the given function is a piecewise function.

Being polynomial functions, each piece is continuous and differentiable.

We will discuss the differentiability of the given function at .

Since the function is piecewise, it is differentiable at  and if and only if the right-hand derivative and left-hand derivative at these points are equal.

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