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Given a point *d where the function f* is continuous,
let's calculate the incremental ratio of the function . We use some properties of the Riemann integral
and the mean value theorem.

where μ is the mean value of the function *f* between
*x* and *d*. This value is enclosed between the
infimum and the supremum of the function in the interval
[*x,d*] or [*d,x*]. The continuity of the function
implies that μ tends to *f(d)* as *x* tends
towards *d*. This proves the theorem.

copyright 2000 et seq. maddalena falanga & luciano battaia

first published on january 07 2003 - last updated on september 01
2003