BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 5, Problem 8RQ
To determine

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

Expert Solution

Answer to Problem 8RQ

The differentiable function f'(x)g'(x) is false for the condition f(x)g(x) in the interval a<x<b.

Explanation of Solution

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).

3>x

Therefore, f(x)>g(x) for each of the values of x in the interval (a,b)=(0,1).

Differentiate f(x)=3 with respect to x.

f'(x)=0 (3)

Differentiate g(x)=x with respect to x.

g'(x)=1 (4)

Equate Equation (2) and Equation (3).

0<1

Therefore, f'(x)<g'(x) so the statement f'(x)g'(x) is false.

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