Question

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

f(x) = 4x² + 3x + 1,    [−1, 1]

a.No, f is continuous on [−1, 1] but not differentiable on (−1, 1).

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

c.Yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on .

d.No, f is not continuous on [−1, 1].

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

2bIf 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.)

Answer 1