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
| Symbol | What it stands for |
|---|---|
| c | Interior point where horizontal tangent |
When to use this
All three hypotheses needed. c is strictly inside (a,b).