Questions: Estimate the AVERAGE rate of change from x=2 to x=5 for the following function f(x) whose graph is given below. (You can click on a graph to enlarge it.) Average rate of change: Note that the average rate of change of a function from x=a to x=b is (f(b)-f(a))/(b-a).

Solution Steps

From the graph, we can see that when $x = 2$, $f(2) = 3$.

From the graph, we can see that when $x = 5$, $f(5) = 7$.

The average rate of change from $x=a$ to $x=b$ is given by $$\frac{f(b)-f(a)}{b-a}$$ In our case, $a=2$ and $b=5$. Therefore, the average rate of change is $$\frac{f(5)-f(2)}{5-2} = \frac{7-3}{5-2} = \frac{4}{3}$$

Final Answer