Teorema di Rolle , dimostrazione teorema di Rolle , esercizi teorema Rolle , nota storica su Dini

Proof of Rolle's theorem, with exercises on Rolle's theorem and some counterexamples. One of the main theorems of differential calculus is Rolle's theorem, although an integral part of this work is also attributed to Ulisse Dini, an Italian mathematician who lived in the second half of the nineteenth century and the early twentieth century. Using this theorem, it is possible to verify the existence of at least one interior point of a given interval in which the derivative takes on a particular value. The lack of one of the hypotheses can compromise the theorem's validity. The geometric significance of the theorem is also interesting. There will be plenty of examples and counterexamples of the theorem, with very simple but non-trivial functions. Rolle's theorem falls into a special case of Lagrange's theorem, which we will illustrate in the lessons following this one. #salvoromeo #teoremadirolle #rolle