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# (Solved): Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?f(x) = x3 ...

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?

f(x) = x3 − 3x + 4, [−2, 2]

A)

Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem.

Yes, f is continuous on [−2, 2] and differentiable on (−2, 2) since polynomials are continuous and differentiable on .

No, f is not continuous on [−2, 2].

No, f is continuous on [−2, 2] but not differentiable on (−2, 2).

There is not enough information to verify if this function satisfies the Mean Value Theorem

B)

If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).

c =

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