extended mean-value theorem

Let f:[a,b] and g:[a,b] be continuousMathworldPlanetmath on [a,b] and differentiableMathworldPlanetmathPlanetmath on (a,b). Then there exists some number ξ(a,b) satisfying:


If g is linear this becomes the usual mean-value theorem.

Title extended mean-value theorem
Canonical name ExtendedMeanvalueTheorem
Date of creation 2013-03-22 13:04:11
Last modified on 2013-03-22 13:04:11
Owner mathwizard (128)
Last modified by mathwizard (128)
Numerical id 9
Author mathwizard (128)
Entry type Theorem
Classification msc 26A06
Synonym Cauchy’s mean value theorem
Synonym extended mean value theorem
Synonym generalized mean value theorem
Related topic MeanValueTheorem