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The proof of the mean value theorem

The proof is a simple consequence of the definition and of the comparison property. Let m and M be the infimum and supremum of the function in [a,b], and consider the two constant functions g(x)=m and h(x)=M. Then g(x)≤f(x)≤h(x) and , that is . The result immediately follows.

copyright 2000 et seq. maddalena falanga & luciano battaia

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