Rolle's theorem
It is part of the basics of mathematical analysis. The theorem (or lemma) of Rolle states that a differentiable function that takes two equal values has at least one 'peak' where its derivative is zero. But who was Michel Rolle? Did you know that he was a fierce opponent of differential calculus? This led to a memorable dispute with Pierre Varignon. With its extension the mean value theorem, Rolle's theorem admits multiple applications: in pure mathematics such as certain methods for solving equations, but also in various fields such as finance for performing certain interest calculations.
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Rolle: a cascade of theorems!
Rolle's theorem, like the celebrated mean value theorem, has been dropped from the secondary-school curriculum. Yet these two major results in analysis are of far more than historical importance. They can be used to solve a great many mathematical problems!
The foundations of differential calculus: the 1700 quarrel | Tangente
A famous scientific quarrel over infinitesimals pitted Rolle against Varignon.
Solving equations: Rolle's theorem to the rescue
The mean value theorem guarantees that very concrete compounding problems do indeed have a solution, and that applying the standard governing equations does indeed lead to that solution. A dream for any economist!