# Whether the statement, if f ′ ( x ) &lt; 0 for 1 &lt; x &lt; 6 then f is decreasing on ( 1 , 6 ) 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 5RQ
To determine

## Whether the statement, if f′(x)<0 for 1<x<6 then f  is decreasing on (1,6) is true or false.

Expert Solution

The given statement is true.

### Explanation of Solution

Reason:

Result used:

1) If f(x)>0 on an interval then f is increasing on that interval.

2) If f(x)<0 on an interval then f is decreasing on that interval.

As it is given that on interval (1,6) the value of f(x)<0 by using decreasing test it can concluded that f is decreasing on (1,6) .

Therefore, the given statement is true.

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