Question: Suppose f C[a, b] and f'(x) exists on (a, b). Show that if f'(x) 0 for all x in (a, b), then there

Suppose f ∈ C[a, b] and f'(x) exists on (a, b). Show that if f'(x) ≠ 0 for all x in (a, b), then there can exist at most one number p in [a, b] with f (p) = 0.

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