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.