Increasing and Decreasing Functions

Definition (Increasing and Decreasing Functions) A function is called increasing on an interval if whenever in   A function is called decreasing on an interval if whenever in

Definition (Increasing and Decreasing Functions) Montonic. A function is called monotonic on an interval if it is either increasing or decreasing on

Proposition (Increasing and Decreasing Functionss) Suppose is continuous on and differentiable on Then,
    
    (i) If for all in then is increasing on
    
    (ii) If for all in then is decreasing on
    

To determine where a function is increasing or decreasing, we begin by finding the critical numbers. These numbers divide the -axis into intervals, and we test the sign of in each of these intervals.

Example (Increasing and Decreasing Functions) Find where the function is increasing and decreasing.

    Solution. Since



To test where the function is monotonic we divide the -axis according to the sign of which depending on the signs of and We put our results into the following table:

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Cite this as:
Increasing And Decreasing Functions
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/increasing-and-decreasing-functions.html