# Math Help - find constants

1. ## find constants

find constants a,b, and c such that the graph of $f(x)=x^3+ax^2+bx+c$ will increase to the point $(-3,18)$, decrease to the point (1,-14) and then continue increasing

2. Originally Posted by euclid2
find constants a,b, and c such that the graph of $f(x)=x^3+ax^2+bx+c$ will increase to the point $(-3,18)$, decrease to the point (1,-14) and then continue increasing
Find the derivative.

$f'(x) = 3x^2 + 2ax + b$

Set this equal to zero at the points $x=-3$ and $x=1$ which will be our critical points.

We get $27 - 6a + b = 0$ and $3 + 2a + b = 0$

Solving these simultaneous equations gives us...

$a = 3$ and $b = -9$.

You can check the second derivative to see that the points $(-3,18)$ and $(1,-14)$ are indeed a max and a min.

Hence we have $f(x) = x^3 + 3x^2 - 9x + c$.

Now just find a value of $c$ that solves...

$-14 = 1 + 3 - 9 + c$ (for the point $(1,-14)$...)

Graph of said function below after you find the $c$ value...