Question

Math

Answer 1

Set f'(x)=0 and find those values of x that are in this interval
$$
f'(x)=3 (x-3) (x+1)
$$
Validate that derivative.

Set it equal to zero. What do you get?

Always plot it.

http://www.wolframalpha.com/input/?i=+x%5E3+%E2%80%93+3x%5E2+%E2%80%93+9x+%2B+2

You can see that this extrema where f'(x)=0 is actually a minimum. So You will need to check the endpoints. Which is larger?

Answer 2

When I set it equal to 0 I get 3 and 1.

Answer 3

Check that the points you get are in the interval [0,6]. You will find, by using the second derivative test, and simply looking at the graph above, that this point is actually a minimum.

So now you'll need to look at the endpoints.

Answer 4

Is f(0) > f(6)? These are the endpoints

Whichever value of x that makes f(x) larger is you maximum, because f'(x) is a minimum.

I hope you see this.