A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
determine the location of each local extrenum of the function f(X)= x^4/4  8X^3/3 +19X^2/2 12X +2
anonymous
 5 years ago
determine the location of each local extrenum of the function f(X)= x^4/4  8X^3/3 +19X^2/2 12X +2

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0take the derivative, set = 0, and solve. The derivative is a cubic polynomial, not easy to find the roots, but you can see by inspection that 1 is a solution. Factor (x1) from your derivative so get \[f'(x)=(x1)(x^27x+12 )= (x1)(x4)(x3))\] therefore zeros are 1,3 and 4. 1 and 4 are relative min, as you can see if you draw a picture of a fourth degree polynomial with positive leading coefficient, and 3 is a relative max

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oops my typo. zeros are 1, 3 and 4, not 1!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that's my problem i'm having trouble setting it to f' how did u get (x1)(x^27x+12)??

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that's my problem i'm having trouble setting it to f' how did u get (x1)(x^27x+12)??

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Find the derivative of each term. After that factor, like in college algebra or precal.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I got it by cheating. It is hard to find the zeros of a cubic polynomial but I figured that this problem was easy so I guessed 1. I checked that f'(1) = 0. Now "factor theorem" says if r is a zero of a polynomial p(x) then p(x) = (xr)q(x) so I knew that f'(x) = (x1) (something) I found the "something" by synthetic division, but you can do long division as well. http://www.youtube.com/watch?v=bZoMz1Cy1T4 Once you have a quadratic you can always find the zeros using the formula but this one factored easily.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.