# Application of mean value theorem

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2. verify that the function f(x) = e^-2x satisfies the hypothesis of mean value theorem on the interval [0, 3] and find all the number c that satisfy the conclusion of the mean value theorem.

3. show that a polynomial of degree two has at most two real roots.

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#### Solution Summary

This solution provides a detailed proof that the given function satisfies the hypotheses of the mean value theorem on the given closed interval of the real line is provided, and the complete set of values of c that satisfy the mean value theorem is determined. Additionally, a prof that a polynomial of degree two has at most two real roots is provided.

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