Function: math[END] - determines extrema at points where a function is not differentiable
Calling Sequence:
END(f, x);
END(f, x=a .. b);
END(f, x, option);
END(f, x=a .. b, option);
Parameters:
f - a real-valued function in x
x
- a name
a, b
- interval boundary points (numerical)
options
- optional arguments
Description:
END determines extrema at those points where a function f in x is not differentiable. In the first and third form, END tries to find all those extrema over the reals; in the second and fourth form only those extrema are returned that exist in the interval a .. b.
By specifying the optional argument 'min', only minima are returned.
By specifying the optional argument 'max', only maxima are returned.
END uses nondiff to determine possible candidates for extrema and evaluates the points p1, .. , pn returned by nondiff by checking whether (f(pk-eps) > f(pk) and f(pk) < f(pk+eps)) or (f(pk-eps) > f(pk) and f(pk) < f(pk+eps)) where eps is a positive small value. By default, END uses the global variable _MathEps to assign eps; by passing the optional argument 'eps'=<value>, however, eps is set <value>.
This function is part of the math package, and so can be used only after performing the command with(math) or with(math, END).
Examples:
> with(math, END):
> END(abs(x), x);
> END(abs(x), x, min);
> END(abs(x), x, max);
> END(abs(ln(x))-(x-1)/(x-2), x, eps=1e-5, min);
See Also:
math/extrema , solve , math/nondiff .
Version History:
Version 1.0 as of January 02, 1998
Version 1.1 as of February 14, 1998
Version 1.1.1 as of December 14, 1998