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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Chapter
Section
BuyFindarrow_forward

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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