Texas Instruments TI-89 and TI-92 Plus Computer 

Last page update: December 21, 1999 
Local Extrema (Minimum, Maximum, and Saddle Points) - for the TI-89 and TI-92 Plus
Version 1.0
Download [ extrema.zip ]
Description Local extrema (minimum, maximum, and saddle points), 2-variable.
Screen shots
Screen image
Documentation Usage:

Expr: A continuous function.

VarList: A list of the independant variables, may be used to select a specific point of evaluation. List only the variables for polynomials and all solutions will be returned. For trigonometric (periodic) functions a general solution is returned, you must select the specific point to evaluate the type of extremum. 

Return value:
A three column matrix. The first two columns are x and y coordinates of the extrema and the third column is a string indicating the type of extremum ("min", "max", "saddle", "periodic" or  if the function (or the specific point tested) has no local extrema). 

1. extrema(x3-3x+y3-3y,{x, y})
    [[-1, 1, "saddle"]
     [ 1, 1, "min"]
     [-1,-1, "max"]
     [ 1,-1, "saddle"]]

2. extrema(cos(y)-cos(x),{x, y})
    [@n2*pi, @n1*pi, "periodic"]

3. extrema(cos(y)-cos(x),{x=pi, y=0})
    [pi, 0, "max"]

4. submat(extrema(x3-3x+y3-3y,{x, y}),1,1,1,2)->vector
    [-1, 1]