# Thread: how to graph function

1. ## how to graph function

a function has a local maximum at x=-2, a local maximum at x=6, and a local minimum at x=1. what does this information tell you about the function? how do i graph this? of what degree would this function be? i started by marking of course x=-2,x=6,x=1 on the graph but unsure of what to do now.

2. I don't think you've got enough information. From what you've been given, your function must be at least a quartic. This means its derivative is at least a cubic and its second derivative is at least a quadratic.

You are told that there is a local maximum at $x = -2$. So $f'(-2) = 0$ and $f''(-2) < 0$.

You are told that there is a local maximum at $x = 6$. So $f'(6) = 0$ and $f''(6) < 0$.

You are told that there is a local minimum at $x = 1$. So $f'(1) = 0$ and $f''(1) > 0$.

Since $f'(-2) = f'(6) = f'(1) = 0$, that means

$f'(x) = a(x - 6)(x - 1)(x + 2)$.

You could expand this, then integrate to find a family of curves for $f(x)$, but unless you are given some points that lie on the curve, you won't be able to evaluate the exact curve.

3. so even something like this would work? Imageshack - graphgr.png - Uploaded by nameme

please excuse the ridiculous graph i'm sure you get the idea