SOLUTION: Find the absolute extreme values of each function on the given interval. f(x)=x^3-6x^2+9x+8 on [-1,2] Please help I am struggling with this chapter. Thanks.

Algebra ->  Graphs -> SOLUTION: Find the absolute extreme values of each function on the given interval. f(x)=x^3-6x^2+9x+8 on [-1,2] Please help I am struggling with this chapter. Thanks.      Log On


   

Question 897313: Find the absolute extreme values of each function on the given interval.
f(x)=x^3-6x^2+9x+8 on [-1,2]
Please help I am struggling with this chapter. Thanks.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Better if you are studying Calculus & Analytical Geometry 1.

df%2Fdx=3x%5E2-12x%2B9=0

x%5E2-4x%2B3=0
x=%284%2B-+sqrt%2816-4%2A3%29%29%2F2
x=%284%2B-+2%29%2F2
highlight_green%28x=1%29 or highlight_green%28x=3%29
Those roots for x are where the extreme values of f will occur.

You are told to find the extreme value on the interval [1,2] and that is where x=1 is.
The x=3 is outside of that interval.
This extreme value at x=1 is highlight%28f%281%29%29=1%5E3-6%2A1%5E1%2B9%2A1%2B8=1-6%2B9%2B8=-5%2B17=highlight%2812%29