Results 1 to 2 of 2

Math Help - Minima problem

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    171

    Minima problem

    THe number of minima of the polynomial 10 x^6 - 24 x^5 + 15 x^4 + 40 x^2 + 108 is ?

    (I took derivative and found a polynomial of degree 5. But making its roots and then testing each one for minima is going to be reaaaly long. Is there some easier way to do this question? )

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,513
    Thanks
    1404
    Quote Originally Posted by champrock View Post
    THe number of minima of the polynomial 10 x^6 - 24 x^5 + 15 x^4 + 40 x^2 + 108 is ?

    (I took derivative and found a polynomial of degree 5. But making its roots and then testing each one for minima is going to be reaaaly long. Is there some easier way to do this question? )

    Thanks
    Do you know the second derivative test?

    If, at a stationary point x = a, f''(a)>0, then a is a minimum.

    So

    f'(x) = 60x^5 - 120x^4 + 60x^3 + 80x.

    Find the stationary points...

    0 = 60x^5 - 120x^4 + 60x^3 + 80x

    0 = 20x(3x^4 - 6x^3 + 4)

    I'll test one of the stationary points for you... Clearly x= 0 is a stationary point.

    So let's take the second derivative, and see what it's sign is when x = 0.


    f''(x) = 300x^4 - 480x^3 + 180x^2 + 80

    f''(0) = 300(0)^4 - 480(0)^3 + 180(0)^2 + 80

    f''(0) = 80 > 0


    Therefore x = 0 is a minimum.

    Test any other stationary points in the same manner.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. maxima minima problem HELP!
    Posted in the Calculus Forum
    Replies: 8
    Last Post: November 11th 2010, 08:52 PM
  2. Maxima and minima trig problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 23rd 2009, 10:12 PM
  3. Maxima / Minima problem?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 31st 2009, 06:27 AM
  4. Easy Maxima minima problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 31st 2007, 05:42 PM
  5. Maxima/minima problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 20th 2006, 04:46 PM

Search Tags


/mathhelpforum @mathhelpforum