Find the critical value(s) of the function by setting the first derivative equal to zero and solving for the x value(s).
A critical value is at 0. Critical values also exist where f(x) is not defined. Therefore there are also critical values at 3 and -3.
If f'(x)>0 the function is increasing on the interval.
If f'(x)<0 the function is decreasing on the interval.
Choose a value for x that is less than -3.
Choose a value for x that is between -3 and 0.
Choose a value for x that is between 0 and 3.
Choose a value for x that is greater than 3.
The function increases in the interval (-`oo,-3).`
The function increases in the interval (-3, 0).
The function decreases in the interval (0, 3).
The function decreases in the interval (3, `oo).`
Because the function changes direction from increasing to decreasing, there is a relative maximum at x=0. The relative maximum occurs at the point (0, 0).