Find min, max of an unfamiliar function

  1. Feb 26, 2012 #1
    1. The problem statement, all variables and given/known data

    For every x over ℝ, find min, max of following expression

    2. Relevant equations

    y=8x4/(x2+1)2+4x/(x2+1)+1

    3. The attempt at a solution
    I've graphed it but it's really complex. How can I find that points? Thank you so much :)
     
  2. jcsd
  3. Feb 26, 2012 #2

    Mark44

    Staff: Mentor

    "every x over ℝ" - this shows up as a box in my browser.
    I'm assuming that you wrote the right side correctly, where there are three terms, with 1 being a term by itself. Rewrite the right side as a single rational expression. What is the least common denominator?
     
  4. Feb 26, 2012 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You need to use Calculus, setting the derivative to zero. That gives you a 4th degree polynomial to solve; its two real roots correspond to the max and min. (They are the roots of the polynomial x4 - 8x3 - 1.)

    RGV
     
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