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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 img, that is img. The result immediately follows.

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