   Chapter 4.2, Problem 33E ### 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

# Let f(x) = l/x and g ( x ) = { 1 x if     x > 0 1 + 1 x if     x < 0 Show that f'(x) = g′(x) for all x in their domains. Can we conclude from Corollary 7 that f − g is constant?

To determine

To show: The statement f(x)=g(x) for all x in their domains and justify it is concluded that fg is a constant.

Explanation

Given:

The functions f(x)=1x and g(x)={1xif  x>01+1xif  x>0

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:

Obtain the derivative of f(x) .

f(x)=ddx(1x)=1x2

Obtain the derivative of g(x) for x>0

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