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Question: suppose that f is differentiable on ab and that for...

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Suppose that f is differentiable on [a,b] and that for all x ∈ [a,b], f′(x) is not equal to 0.

(a) Prove that either f′(x) > 0 for all x ∈ [a,b] or f′(x) < 0 for all x ∈ [a,b].

(b) Prove that either f is strictly increasing on [a, b] or f is strictly decreasing on [a, b]. (Hint: Mean Value Theorem)

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