# Maxima and Minima

• Jun 8th 2010, 03:22 PM
Esthephane
Maxima and Minima
Consider the functionn, find the critical points of f(x) and determine the local maxima and minima. (give both x and y coordinates) on the given interval. part (b) Find the absolute maxima and minima of f(x)(give both x and y coordinates) on the given interval.

f(x)=x^3-6x^2+9x+2 on the interval [-1,4]

For this problem, I took the derivative of f(x).
f'(x)=3x^2-12x+9
Then i Made a table and plugged in all the numbers within -1-4. Then i'm stuck.
• Jun 8th 2010, 03:50 PM
TheCoffeeMachine
Quote:

Originally Posted by Esthephane
f'(x)=3x^2-12x+9

You need to find the zeros of f'(x).
• Jun 8th 2010, 03:54 PM
Esthephane
How to I find the 0's? f'(0)?
• Jun 8th 2010, 03:59 PM
TheCoffeeMachine
Quote:

Originally Posted by Esthephane
How to I find the 0's? f'(0)?

What happens at critical points? At a critical point, \$\displaystyle f'(x) = 0\$. So to find them, we find \$\displaystyle f'(x) \$ (which you have already done), set it equal to zero, and then solve for \$\displaystyle x\$. The zeros of \$\displaystyle f'(x) \$ are the roots of \$\displaystyle f'(x)\$, i.e. when \$\displaystyle 3x^2-12x+9= 0\$. Can you find the two roots of the quadratic equation?