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

1. ## 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!

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.

2. What are the derivatives at those locations?

3. Originally Posted by dwsmith
What are the derivatives at those locations?
Sorry, I updated my post

4. Originally Posted by razr
Sorry, I updated my post
The question still stands.

5. $f'(-2)=f'(6)=f'(1)=0$

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

$\displaystyle f(x)=\int f'(x)dx$

6. 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"!)

7. 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.)