Find Absolute Maxima and Minima of f(x) on [-2,2]

[the_ace]

1. Find the absolute maxima and the absolute minima of the following function

f(x)=(2x)/(x^2+1) on [-2,2]

 

[the_ace]

i found the derivative = (2x^2-2)/(x^2+1)^2

 

[physicsnoob93]

Okay, what will the derivative be at a maximum point?

 

[the_ace]

I can't solve it

 

[physicsnoob93]

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

It's important to understand what the assignment is on before attempting it.