Question

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

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

f(x) = x3 + x − 5,    [0, 2]

a) No, f is continuous on [0, 2] but not differentiable on (0, 2).

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

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

d) Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on .

e) No, f is not continuous on [0, 2].
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 = ??????????

2. If f(4) = 1 and f '(x) ≥ 1 for 4 ≤ x ≤ 9, how small can f(9) possibly be?

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