## 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 Documentation Usage: extrema(Expr,VarList)->Matrix 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).  Examples: 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]