Function: math[diffquot], math[diffquotfn] - determine difference quotient

Calling Sequence:

diffquot(f, x, 'var');
diffquot(f, x=a, 'var');
diffquotfn(f, x, 'var');
diffquotfn(f, x=a, 'var');

Parameters:

f - an algebraic expression
x - the name of the indeterminate in f
a - a point of type algebraic
'var' - (optional) a name

Description:

diffquot and diffquotfn determine the difference quotient of a function f in one real. The difference quotient (ratio of change) is defined as

[Maple Math] .

In the first form the general difference quotient is returned as a term.

In the second form, the difference quotient about a point a is determined.

By default, the null sequence h is returned as the name 'h'. By giving an optional third argument you may choose another name.

diffquotfn works as described before but returns an anonymous function.

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

Examples:

> with(math):

> dq1 := diffquot(x^2, x);

[Maple Math]

> limit(dq1, h=0);

[Maple Math]

> dq2 := diffquot(x^2, x=1);

[Maple Math]

> subs(h=0, dq2);

[Maple Math]

> f1 := diffquotfn(sqrt(x), x=c, 'p');

[Maple Math]

> limit(f1(p), h=0);

[Maple Math]

See Also:

diff , student/slope , math/ex , math/inflection .

Version History:

Version 1.0 - December 14, 1998