   Chapter 4.2, Problem 32E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# If f′(x) = c (c a constant) for all x, use Corollary 7 to show that f(x) = cx + d for some constant d.

To determine

To show: The statement f(x)=cx+d for some constant d if f(x)=c where c is constant for all x.

Explanation

Corollary used:

“If f(x)=g(x) for all x in an interval (a,b), then fg is constant on (a,b), that is f(x)=g(x)+c where c is constant”.

Proof:

From the given condition, it is observed that f(x)=c.

In order to use the corollary mentioned above, define the function g(x) to be g(x)=cx for all x and for a constant c

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 