7. Let f be differentiable on (a, b), continuous on [a, b], with f (a) = f...
Question:
7. Let f be differentiable on
(a, b), continuous on [a, b], with f
(a) = f
(b) = O.
Prove that if f
(c) > 0 for some c E
(a, b), then there exist Xl, x2 E
(a,
b) such that f'(xd > 0 > f'(X2).
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