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What is the constant function theorem

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Reference no: EM131602912

Question: 1. Prove that if f'(x) = g'(x) for all x in (a, b), then there is a constant C such that f(x) = g(x) + C on (a, b). [Hint: Apply the Constant Function Theorem to h(x) = f(x) - g(x).]

2. Suppose that f'(x) = f(x) for all x. Prove that f(x) = Cex for some constant C. [Hint: Consider f(x)/ex.]

Reference no: EM131602912

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