Average and Instantaneous Rates of Change

I. For a linear function, the average rate of change over any interval is equal to the instantaneous rate of change at every point.

II. For any nonlinear function, the average rate of change over an interval is equal to the instantaneous rate of change at the midpoint of that interval.

III. For any differentiable function $f$, its instantaneous rate of change at a point $x$ is given by $\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$.

Which of the statements above is/are true?