Question

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?

Answer 1