7. Let f be differentiable on (a, b), continuous on [a, b], with f (a) = f...

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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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