# A function has a local maximum at x=-2, 6, and a local minimum at x=1.

• Jan 4th 2011, 08:23 PM
razr
A function has a local maximum at x=-2, 6, and a local minimum at x=1.
I can't solve this question, I need some help! Please sketch the graph if you can! (Nod)

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? Sketch a possible function that has these characteristics.
• Jan 4th 2011, 08:29 PM
dwsmith
What are the derivatives at those locations?
• Jan 4th 2011, 08:31 PM
razr
Quote:

Originally Posted by dwsmith
What are the derivatives at those locations?

Sorry, I updated my post
• Jan 4th 2011, 08:32 PM
dwsmith
Quote:

Originally Posted by razr
Sorry, I updated my post

The question still stands.
• Jan 4th 2011, 10:01 PM
dwsmith
$f'(-2)=f'(6)=f'(1)=0$

$f'(x)=a(x+2)b(x-6)c(x-1)=abcx^3-5abcx^2-8abcx+12abc \ \ a,b,c\in\mathbb{R}$

$\displaystyle f(x)=\int f'(x)dx$
• Jan 5th 2011, 02:27 AM
HallsofIvy
Notice that the problem says "sketch a possible function". There are an infinite number of such functions, you should try graphing the simplest one. What does a graph look around a minimum or maximum? Notice that you are not given the value of the function at x= 1, -2, or 6 so you can take them to be whatever you want. (The "local minimum" can be higher than the "local maxima"!)
• Jan 5th 2011, 02:34 AM
DrSteve
Note that the derivatives at these points can also be infinite of undefined. If the derivative is infinite there is a cusp. If the derivative is undefined there is a sharp edge. (There are other possibilities for undefined derivatives, but in the other cases there would be no min or max.)