Function: math[inflection] - find inflection points of a function

Calling Sequence:

inflection(f, x);
inflection(f, x, options);
inflection(f, x=a .. b);
inflection(f, x=a .. b, options);

Parameters:

f - an algebraic expression in x
x - a name
a, b - interval boundary points (numerical)

Description:

inflection searches for inflection points of a function in one real variable on an interval [a, b].

If no range is specified and f does not include a trigonometric function, then inflection searches over the reals (=RealRange(-infinity, infinity)).

If no range is specified and f does include a trigonometric function, then the default range is given by the global variable _MathDomain (-10 .. 10 by default).

inflection is an interface to the function math[extrema], so you may pass all the options to inflection that exist in function extrema. The options 'ALL', 'MIN', 'MAX', 'all', 'min', or 'max' are ignored if given as optional arguments to inflection.

See ? math,extrema for further information and optional arguments.

This function is part of the math package, and so can be used only after performing the command with(math) or with(math, inflection).

Examples:

> inflection(0.8*x^3-0.2*x^4-2, x);

[Maple Math]

> _MathDomain;

[Maple Math]

> inflection(x^2*sin(x), x, eps=1e-5);

[Maple Math]
[Maple Math]

> inflection(tan(x), x=0 .. 10);

[Maple Math]

See Also:

math/extrema , math/fnull .

Version History:

Version 1.00 - May 26, 1997

Version 2.00 - December 30, 1997