Answer
(a) $10$
(b) $[10, 50]$
(c) $[40, 60]$
(d) $-10$; this represents the average rate of change of $f$ on the interval $[10, 40]$.
Work Step by Step
(a) $\frac{f(60) - f(20)}{60 - 20} = \frac{700 - 300}{40} = 10$
(b) $\frac{f(50) - f(10)}{50 - 10} = \frac{400 - 400}{40} = 0$
(c) $\frac{f(60) - f(40)}{60 - 40} = \frac{700 - 200}{20} = 25$
$\frac{f(70) - f(40)}{70 - 40} = \frac{900 - 200}{30} = 23.33$
$25\gt233.33$ so $[40, 60]$ has a greater average rate of change.
(d) $\frac{f(40) - f(10)}{40 - 10} = \frac{100 - 400}{30} = -10$
This represents the change in the $y$ value over the change in $x$ value, and thus represents the average rate of change on the interval $[10, 40]$.
