Answer
(a) 10
(b) $[10,50]$
(c) The interval $[40,60]$ has a greater average rate of change.
(d) -6.7
This value represents the slope of the straight line drawn from the point $(10, 400)$ to the point $(40, 200)$, which is the average rate of change.
Work Step by Step
(a) $f(60) = 700$
$f(20) = 300$
We can find the average rate of change:
$\frac{f(60)-f(20)}{60-20} = \frac{700-300}{60-20} = 10$
(b) $f(10) = f(50) = 400$
In the interval $[10, 50]$, the average rate of change is 0.
(c) $f(70) = 900$
$f(60) = 700$
$f(40) = 200$
We can find the average rate of change in the interval $[40,60]$:
$\frac{f(60)-f(40)}{60-40} = \frac{700-200}{60-40} = 25$
We can find the average rate of change in the interval $[40,70]$:
$\frac{f(70)-f(40)}{70-40} = \frac{900-200}{70-40} = 23.3$
The interval $[40,60]$ has a greater average rate of change.
(d) $f(40) = 200$
$f(10) = 400$
We can compute:
$\frac{f(40)-f(10)}{40-10} = \frac{200-400}{40-10} = -6.7$
This value represents the slope of the straight line drawn from the point $(10, 400)$ to the point $(40, 200)$
