• Support PF! Buy your school textbooks, materials and every day products Here!

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

  • #1

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]
 

Answers and Replies

  • #2
Buzz Bloom
Gold Member
2,211
365
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
 
  • #3
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,544
756

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]
Please read the posting guidelines. Specifically, you are requested not to use large or bold face fonts, nor to post equations in the subject line of the post.
 

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

Replies
5
Views
9K
Replies
5
Views
12K
  • Last Post
Replies
11
Views
3K
Replies
15
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
9
Views
4K
Replies
2
Views
6K
  • Last Post
Replies
1
Views
2K
Top