Absolute maxima

  • Thread starter the_ace
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  • #1
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1. Find the absolute maxima and the absolute minima of the following function

f(x)=(2x)/(x^2+1) on [-2,2]
 

Answers and Replies

  • #2
7
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i found the derivative = (2x^2-2)/(x^2+1)^2
 
  • #3
Okay, what will the derivative be at a maximum point?
 
  • #4
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I cant solve it
 
  • #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.
 
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