# Whether the statement, if the function f is positive increasing and function g is positive increasing then fg is also increasing 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 14RQ
To determine

## Whether the statement, if the function f is positive increasing and function g is positive increasing then fg is also increasing is true or false.

Expert Solution

The given statement is true.

### Explanation of Solution

If a function f is increasing then f(x)>0 for all values of x

Similarly, if a function g is increasing then g(x)>0 for all values of x

Show that (fg)>0 for all values of x.

The product function (fg) can be expressed as,

(fg)=fg+gf>0

Hence, (fg)>0 .

Therefore, the product function, fg is an increasing function.

Thus, the given statement is false.

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