Rolle's theorem (Continuous on [a,b], differentiable on (a,b), f(a)=f(b) ⇒ ∃c in (a,b))

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Continuous on [a,b], differentiable on (a,b), f(a)=f(b) ⇒ ∃c in (a,b): f'(c)=0

What each symbol means

SymbolWhat it stands for
cInterior point where horizontal tangent

When to use this

All three hypotheses needed. c is strictly inside (a,b).