- #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]

- Thread starter the_ace
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- #1

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

- #2

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

- #3

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

- #4

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I cant solve it

- #5

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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.

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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