MAPLE: Extreme Values of Functions

1. Example: a function of one variable. Here
   f(x) = x³ - 4x² + x - 3

   > readlib(extrema);

   > f:= x^3 - 4*x^2 + x - 3;

   > ex:= extrema(f,{},{x},'s'); stores the extreme value of f in ex

   > evalf(ex); displays the extreme value in decimal form

   > s; s contains the critical point(s) of f

   > evalf(s); displays the critical point(s) in decimal form

   The quantity s contains the critical point(s).

   The quantity ex contains the extreme value of f.

2. Example: a function of two variables. Here

   > readlib(extrema);

   > f:= -x/3 -y/6 +7/30*y^2 +3/2 +17*x*y/30 +x^2/2;

   > ex:= extrema(f,{},{x,y},'s');

   > evalf(ex); displays the extreme value in decimal form

   > s; the critical point(s) of f

   > evalf(s); displays the critical point(s) in decimal form

3. NOTE: Also see the commands minimize and maximize under the student library. These give minima and maxima only; they do not give critical points.

   > with(student);

   > ?minimize;

   > ?maximize;

4. For many other popular commands common to student use,

   > ?student;

Written and Maintained by

Prof. Kevin G. TeBeest
Applied Mathematics
Kettering University

Last modified: 07/23/07

Copyright © 1997–2023 Kevin G. TeBeest. All rights reserved.