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 11RQ
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 true.

Explanation of Solution

Reason:

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) , since the functions f(x) and g(x) are increasing.

The sum of the function (f+g)(x) can be expressed as follows.

(f+g)(x1)=f(x1)+g(x1)<f(x2)+g(x2)=(f+g)(x2)

Thus, (f+g)(x) is an increasing function on I.

Therefore, the given statement is true.

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