Function: math[monotony] - Determine monotony

Calling Sequence:

monotony(expr, x=a .. b);

Parameters:

expr - an algebraic expression

x - indeterminate in expr (of type name)

a, b - realcons

Description:

The function determines the monotony of a function in one real on the given interval [a, b].

The return is a sequence of equations. The left-hand side of each equation contains the subinterval [p, q] where a specific monotony has been found, expressed in a call to RealRange. The left-hand side contains an integer value v. If v = -1, then the function expr is decreasing on [p, q]; if v=0, the function is constant; if v = 1, the function is increasing an [p, q].

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

Examples:

> restart: with(math, monotony):

> monotony(x^2, x=-1 .. 0);

[Maple Math]

> monotony(x, x=-1 ..1 );

[Maple Math]

> monotony(0.8*x^3-0.2*x^4-2, x=-10 .. 10);

[Maple Math]

> monotony(1, x=-10 .. 10);

[Maple Math]

> monotony(abs(x), x=-10 .. 10);

[Maple Math]

> monotony(sin(x), x=0 .. Pi);

[Maple Math]

See Also:

Version History:

Version 1.0 - July 22, 2000