Finding local maximums and minimums

[wildcat12]

Homework Statement

Find a cubic function g(x)=ax^3 +bx^2 +cx +d that has a local maximum value of 2 at -9, and a local minimum value of -7 at 8.

Homework Equations

The Attempt at a Solution

I thought i would find the derivative and set it equal to zero, but i do not know what to do from there

 

[micromass]

Well, to find the values of a,b,c,d you'll need some constraints on those numbers

1) You know that when you plug 2 in your poly, you should get -9. When you plug -7 in, you would get 8. These deliver two equations.

2) When you derive your function, you know that when you plug 2 in, you get 0. When you plug -7 in, you would get 0 to. These deliver another two equations.

So you have 4 equations. You should be able to solve this system without problems...

 

[wildcat12]

So plug those numbers in for x? correct?

 

[micromass]

yes!

 

[wildcat12]

Awesome. i don't know why i didnt get that