Question

(Question Closed)

Answer 1

Ok so Rolle's theorem is a special case of MVT, where you take \[f(a)=f(b)\], which simplifies things out a little bit

Answer 2

Well, at first, we have to note that for a differentiable function f, on interval (a,b) and continuous over [a,b] and f(a)=f(b) you have:

Role's: at least 1 horizontal tangent to the curve on the interval
Mean: at least 1 point where instantaneous slope = slope of the secant.

An application outside mathematics idea I can start to think of is a Roller Coaster, for example.

Answer 3

Intuitively, Rolle's thm says that if you have two points with the same y value, then somewhere between them exists a point at which the derivative of the function must be zerom i.e.