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);
> monotony(x, x=-1 ..1 );
> monotony(0.8*x^3-0.2*x^4-2, x=-10 .. 10);
> monotony(1, x=-10 .. 10);
> monotony(abs(x), x=-10 .. 10);
> monotony(sin(x), x=0 .. Pi);
See Also:
Version History:
Version 1.0 - July 22, 2000