Monotonicity Gallery
The following is a gallery of demos for illustrating monotonicity. These figures and animations can be used by instructors in a classroom setting or by students to aid in understanding the concepts of increasing and decreasing. Two file formats, gif and mov are available.
The gif animations should run on most systems and the file sizes are relatively small.
The mov animations require the QuickTime Player (version 6) which is a free download available by clicking here; these files are also small. (The mov files may not execute properly in older versions of QuickTime.)
The collection of animations in gif and mov format can be downloaded; see the zipped download category at the bottom of the following table.
All the animations were generated from Excel files which can also be downloaded.
We use + to indicate increasing and  for decreasing at points along the curve.
Gallery of Animations

f(x) = x 

f(x) = x^{2} + 4


f(x) = 1/x


f(x) = cos(pi x)


f(x) = x^{3} + 4


f(x) = cos(pi x) + sin(pi x)


f(x) = 2x^{4}  x^{2}
+ 1


f(x) =x^{3}/3  3x^{2}
+ 8x + 3


f(x) =(x^{2} 12)x


f(x) = x^{4}  2x^{3}
+ 3

f(x) = (x + 1)^{2}(2 
x)

To download the gif and Quicktime animations click here.
To download the the individual Excel files click here.
To download or run an Excel file containing all 11 demos click here.
This gallery was developed by David R. Hill, Temple University.

DRH Last updated 9/27/04