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Lagrange's Theorem: demonstration of Lagrange's theorem and various exercises on Lagrange's theorem with examples and counterexamples. After having dealt with Rolle's theorem, it is time to deal with another of the most important theorems of differential calculus, which represents a more general case of Rolle's theorem. The hypotheses are (almost) the same as those seen in Rolle's theorem with the exception of a missing hypothesis that generalises the theorem. For the demonstration we will use an auxiliary function that respects all the hypotheses of Rolle's theorem and we will easily arrive at the thesis. There will be no shortage of examples and counterexamples that will help to understand how to deal with the exercises. #salvoromeo #teoremalagrange