Theorem Let
f:[a,b]-->R be
continuous on
[a,b]
and
differentiable on
(a,b). Further suppose that
f(a)=f(b)=0. Then there exists
c in
(a,b)
such that the derivative
f '(c)=0.
Here's a diagram to illustrate the theorem.
| .-.
| / \
| / \
---a---c---b-------
|
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