1. ## 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.

2. Originally Posted by Esthephane
f'(x)=3x^2-12x+9
You need to find the zeros of f'(x).

3. How to I find the 0's? f'(0)?

4. 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?