Whether the statement “If f and g are increasing on an interval I , then f − g is increasing on I ” is true or false.

Single Variable Calculus: Concepts...

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

Single Variable Calculus: Concepts...

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

Solutions

Chapter 4, Problem 12RQ
To determine

Whether the statement “If f and g are increasing on an interval I, then f−g is increasing on I” is true or false.

Expert Solution

The given statement is false.

Explanation of Solution

Given that the functions f(x) and g(x) are increasing on an interval I.

Let x1<x2 where x1,x2I.

Then, f(x1)<f(x2) and g(x1)<g(x2).

The subtraction of the function (fg)(x) can be expressed as follows.

(fg)(x1)=f(x1)g(x1)>f(x2)g(x2)>(fg)(x2)

Thus, (fg)(x) is not an increasing function on I.

Therefore, the given statement is false.

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