1. Let f be a twice-differentiable function such that f (2) = 8 and f (4) = 5. Which of the following must be true for the function f on the interval 2 ≤ x ≤ 4.

Question

1. Let f  be a twice-differentiable function such that f (2) = 8 and f (4) = 5. Which of the following must be true for the function f on the interval 2 ≤ x ≤ 4.
I. The average value of f  is 6.5
II. The average rate of change of f  is -1.5
III. The average value of f ' is -1.5

Select one:
a. I, II, and III
b. I and II only
c. II only
d. II and III only
e. III only

Steve · Answer

the average value of f' on the interval is ∫ f' dx = (f(4)-f(2))/(4-2) = -3/2 Since II and III say the same thing, I pick (D) we know nothing about the average value of f.