Rolle’s Theorem

Rolle's Theorem

A theorem of calculus that ensures the existence of a critical point between any two points on a "nice" function that have the same y-value.

Rolle's Theorem: If f is continuous on [a,b], differentiable on (a,b), and f(a)=f(b), then f'(c)=0 for some c in (a,b).
Graph of y=f(x) with points (a,f(a)), (b,f(b)) at equal heights and (c,f(c)) between them where f'(c)=0.

See also

Continuous, differentiable, slope, mean value theorem