Question: Suppose that 0 f(t) Meat and 0 f'(t) Keat for t 0, where f' is continuous. If the Laplace transform

Suppose that 0 ≤ f(t) ≤ Meat and 0 ≤ f'(t) ≤ Keat for t ≥ 0, where f' is continuous. If the Laplace transform of f(t) is F(s) and the Laplace transform of f'(t) is G(s), show that
G(s) = sF(s) = f(0) , s > a

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