   Chapter 5, Problem 8RQ ### 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

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f and g are differentiable and f(x) ≥ g(x) for a < x < b, then f′(x) ≥ g′(x) for a < x < b.

To determine

If f(x)g(x) in the interval a<x<b then f'(x)g'(x) is true or false.

Explanation

Given information:

The functions f and g in the interval a<x<b has f(x)g(x) (1)

Check the differentiation with f'(x)g'(x) (2)

Calculation:

Check the statement is true or false using an example as shown below:

Let assume a=0,b=1,f(x)=3,g(x)=x.

Substitute 3 for f(x) and x for g(x) in Equation (1)

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