One of the questions on (the version I got) of this quiz is defective:
Problem 7: Which of the following facts about the functions x^2 in the interval [-2,2] follows from the mean value theorem?
None of the proffered answers is correct! Yes, the functions is continuous on the given closed interval and differentiable on its interior. The MVT then gives the EXISTENCE of SOME point c in the interior at which the derivative is the slope of the tangent line. The intended answer would seem to be "Tangent to x^2 at x = 0 has a slope of 0", but this is NOT a conclusion that may be obtained by using the mean value theorem. The theorem is a pure existence theorem!
