We are about to learn integrals, but this homework does not expect an understanding of them. I'm having a hard time understanding what I am to do.

The problem asks me to find cubic function in the form of that has a local maximum value of 9 at -3 and a local minimum value of 7 at 0.

So I knew that the zeros for were equal to -3 and 0. Using that I came up with . I realize though that any coefficient attached to the first x would still give a zero of 0. So how do I find that coefficient?

Taking the antiderrivitive of my function, then adding the constant 7 gave: . However with this, , not 9. What am I missing?

Thanks in advance!

EDIT:

I wanted to add that I tried also working from the second derivative, too. Thinking that the inflection point ought to be halfway between 0 and -3, I made which makes which still has zeros of 0 and -3. The anti derivative of that gives after adding the constant. We're really close, but which isn't 9.

Just wanted whoever to know that I'm giving it the old college try