for some constant
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
Take the derivative of . As BobP said, that's equal to . That gives you a relationship between a and c, so you have only two unknowns. The equation gives you d, and the equation then gives you a and c.
- Hollywood
I must be extremely thick headed. I'm sorry, but I still don't get it. The derivative of is , but 'C' isn't the 'c' from the first equation, is it? I can't see how it would be. I tried setting it up another way where which leaves me with but I'm not sure I'm helping myself here. I'm getting frustrated because I feel like it should be obvious, but it isn't at all.
Thanks everyone. I got it figured out thanks to your help. I was frustrated because everyone kept telling me what I already knew and had said in post 1, that is, that . I just didn't realize that I needed to take the equation to go to I set that equal to 9, solved for C which was meaning and . Thanks again.