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Absolute maxima

  1. Oct 8, 2009 #1
    1. Find the absolute maxima and the absolute minima of the following function

    f(x)=(2x)/(x^2+1) on [-2,2]
     
  2. jcsd
  3. Oct 8, 2009 #2
    i found the derivative = (2x^2-2)/(x^2+1)^2
     
  4. Oct 8, 2009 #3
    Okay, what will the derivative be at a maximum point?
     
  5. Oct 8, 2009 #4
    I cant solve it
     
  6. Oct 8, 2009 #5
    A maximum would occur if the derivative exists and changes sign from positive to negative at a certain point.

    A minimum would occur if the derivative exists and changes sign from negative to positive at a certain point.

    This means the derivative must pass through zero to change the sign. So, equate your derivative to zero and solve for the x coordinates of these points. In Calculus, these points are called critical points.

    Just in case you don't understand, I'd recommend the following resources:

    http://ltcconline.net/greenl/courses/115/applications/frsttst.htm
    http://www.math.wvu.edu/~hjlai/Teaching/Tip-Pdf/Tip1-21.pdf
    http://www.math.ucdavis.edu/~xiaoh/16a/extrema.pdf [Broken]

    It's important to understand what the assignment is on before attempting it.
     
    Last edited by a moderator: May 4, 2017
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