Find min, max of an unfamiliar function

  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. 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. Ray Vickson

    Ray Vickson 5,870
    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
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook