# Rolle's Theorem

Rolle's Theorem

Rolle's theorem states that if a function is continuous on and differentiable on with , then there is at least one value with where the derivative is 0. In terms of the graph, this means that the function has a horizontal tangent line at some point in the interval.

f

[a,b]

(a,b)

f(a)=f(b)

x

c

a<c<b

c

Rolle's theorem can be thought of as a lemma or a corollary of the mean value theorem in calculus.