Chapter 6, Problem 1SYU

To determine

Whether the given statement is true or false.

Answer to Problem 1SYU

True.

Explanation of Solution

Given information:

A statement is given as -

"If a function f is positive on an interval, then its anti derivatives are all increasing on that interval"

Calculation:

Let us suppose $F$ is the anti derivative of a derivative function $F\text{'}=f$, then below results can be observed from the graph of derivative f :

$1.)$ If $f>0$ on an interval, then $F$ is increasing on that interval.

$2.)$ If $f<0$ on an interval, then $F$ is decreasing on that interval.

$3.)$ If $f=0$ on an interval, then $F$ is constant on that interval.

Thus, given statement is true.