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).

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).

Transcript text: 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: $\square$ Note that the average rate of change of a function from $x=a$ to $x=b$ is $\frac{f(b)-f(a)}{b-a}$.

Solution

Solution Steps

Step 1: Find the value of f(2)

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

Step 2: Find the value of f(5)

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

Step 3: Calculate the average rate of change.

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

The average rate of change from $x=2$ to $x=5$ is $\boxed{\frac{4}{3}}$.

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