Let g(x) = 2ˣ
Can we use the mean value theorem to say the equation g'(x) = 16 has a solution where 3 A. No, since the function is not differentiable on that interval.
B. No, since the average rate of change of g over the interval 3 < 3 < 5 isn't equal to 16.
C. Yes, both conditions for using the mean value theorem have been met.