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

[brandon cheatham]

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.

Homework Equations

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]

 

[Buzz Bloom]

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 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.

Homework Equations

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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