How Do You Find Absolute Extrema of a Polynomial Function?

[chaosblack]

simple SIMPLE local extremia question

Homework Statement

Find the absolute maximum and absolute minimum values of f(x) = 3x^4 - 8x ^3 + 12x^2 -48x +25, where 0 <= x <= 3.

Homework Equations

N/a

The Attempt at a Solution

f'(x) = 12x^3 - 24x^2 + 24x -48
= 12 (x^3 - 2x^2 + 2x -4)
= 12 (x-2) (X^2 +2)

I know how to do the rest, but just wondering before I go on... What should i do with that one factor...do I omit the (x^2 +2)?

 

[jhicks]

Well beside your first three lines of solution being irrelevant, it looks correct to me.

Edit: Actually you forgot a factor of 2 in your final h solution according to the symbolic result you derived earlier on.

 

[chaosblack]

Okay thanks a lot, I updated the thread with a different question lol

 

[jhicks]

Well you know that the absolute maximum/minimum lies at a place where the derivative is 0 or at the endpoints of the interval. Does x^2+2=0 have a real solution?

 

[chaosblack]

haha...thanks man. I'm starting to forget to most simple stuff