Consider the function below. (If an answer does not exist, enter DNE.) F(x) = x 9 − x (a) Find the interval of increase. (Enter your answer using interval notation.)

Step-by-step explanation:

The first step to solve this question is finding the critical points of the function F(x), which are x for which:

In this question:

So

So we have three intervals:

We take a value of x from each interval. If the derivative is positive, the function increases. Otherwise, it decreases.

First interval:

Will take x = -1.

Positive, so increases.

Second interval:

(-0.76, 0.76),

Will take x = 0;

Negative, so decreases

Third interval:

Will take x = 1

Positive, so increases.

Interval of increase:

First and third, so:

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