1 Let f: [0, co) →R be a differentiable function. (a) if f is order exponential, prove that f is also order exponential, by using the mean value theorem and the fact that t2 Vt >0 e - 1+t + + > 1+t>t 2! (b) If f is order exponential, does this imply that f' is order exponential? Prove or supply a counterexample.

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A: We will find out the required expression.

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