## Thomas' Calculus 13th Edition

The fundamental theorem of calculus states that the average value of any function $f(x)$ on the interval $[p,q]$ can be defined as: $\dfrac{1}{q-p}\int_p^q f'(x) dx=\dfrac{1}{q-p}[f'(x)]_p^q$ or, $=\dfrac{f(q)-f(p)}{q-p}$ Thus, this shows the average change of $f(x)$ on $[p,q]$.