Average value of rate of change and of a function.?

Question

Let f be a twice differentiable function such that f(1) = 2 and f(3) = 7. Which of the following must be true for the function f on the interval 1 <= x <= 3 ?

I: The average rate of change of f is 5/2.
II: The average value of f is 9/2.
III: The average value of f' (the derivative) is 5/2.

Any help would be appreciated ^_^

Answer 1

Choice 3.

Answer 2

All three are true.

I take 'twice differentiable' to mean it is a linear function, that is to say it is of the form f(x) = mx + b. The slope from 1,2 to 3,7 is 5/2, which is same as avg. rate of change, which is same as derivative. Finally, the average of 7 and 2 is 4.5 .