(6 points) Suppose the function f: R→ R is differentiable and that {Xn}n=1,2,... is a strictly increasing bounded sequence with f(xn) ≤ f(xn+1) for all natural numbers n. Prove that there is a number xo at which f'(xo) ≥ 0. (Hint: Use the Monotone Convergence Theorem)

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