Problem 1. Let m, n be nonnegative integers, and let ao, …, am and bo, …, bn be real numbers. Considerthe real-valued polynomial functionsmf (x) = do +Aajxig(x) = bo +Mbixij=1j=1You know from Calculus I that the functions f and g are differentiable. Assume that m and n are theresult.degrees for f and g, respectively, and use what you know about derivatives to help prove the followingIf f (x) = g(x) for all real numbers x, then m = n, and a; = bi for 1 < j <m.
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