# How to find absolute min/max of f(x)=x^3+3x^2-24x+1 on[-1,4]

## Homework Statement

How to find absolute min/max of f(x)=x^3+3x^2-24x+1 on[-1,4]
I need to find the absolute min and absolute max.

## The Attempt at a Solution

I first took the derivative, reduced, and set it to equal 0 to find crit numbers.
x^2+2x-8=0
Factored.
(x+4)(x-2) = 0
so x=-4 or x=2 but since -4 is not on the interval i threw it out and kept 2 as my only crit #
I plugged in my critical number along with my LB and RB numbers to find:
Aboslute Max. to be (-1,23)
Absolute Min. to be (2-27)

Am I doing this correctly? This was a take home quiz given in my calculus class and I want to make sure it is correct before I turn it in. Thanks! 234
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Buzz Bloom
Gold Member
Hi brandon:

You need to include the end points of the range, -1 and 4, whether or not they derivative is zero for those values. Then you need to evaluate f(x) at the derivative's zeros and at the boundaries.

Regards,
Buzz

LCKurtz
Homework Helper
Gold Member

## Homework Statement

How to find absolute min/max of f(x)=x^3+3x^2-24x+1 on[-1,4]
I need to find the absolute min and absolute max.

## The Attempt at a Solution

I first took the derivative, reduced, and set it to equal 0 to find crit numbers.
x^2+2x-8=0
Factored.
(x+4)(x-2) = 0
so x=-4 or x=2 but since -4 is not on the interval i threw it out and kept 2 as my only crit #
I plugged in my critical number along with my LB and RB numbers to find:
Aboslute Max. to be (-1,23)
Absolute Min. to be (2-27)

Am I doing this correctly? This was a take home quiz given in my calculus class and I want to make sure it is correct before I turn it in. Thanks! 234[/B]
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