the graph of a function f is shown.\n(a) find the average rate of change of f on the interval 10, 60.\n(b)…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$.

Step2: Solve part (a)

For the interval $[10,60]$, assume from the graph that $f(10)\approx400$ and $f(60)\approx700$. Then the average rate of change is $\frac{f(60)-f(10)}{60 - 10}=\frac{700 - 400}{50}=\frac{300}{50}=6$.

Step3: Solve part (b)

The average rate of change $\frac{f(b)-f(a)}{b - a}=0$ when $f(b)=f(a)$. Looking at the graph, on the interval $[10,50]$, the function has the same $y$ - values at the endpoints.

Step4: Solve part (c)

The expression $\frac{f(40)-f(0)}{40 - 0}$ represents the slope of the line segment connecting the points $(0,f(0))$ and $(40,f(40))$ on the graph of the function $y = f(x)$ according to the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Answer:

(a) 6 (b) [10, 50] (c) $\frac{f(40)-f(0)}{40 - 0}$ represents the slope of the line segment from $(0,f(0))$ to $(40,f(40))$