consider the graph of ( f(x) ).\nwhat is the average rate of change of ( f(x) ) from ( x_1 = 4 ) to ( x_2 =…

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = f(x)) from (x_1) to (x_2) is (\frac{f(x_2)-f(x_1)}{x_2 - x_1}).

Step2: Identify the values of (f(x_1)) and (f(x_2))

From the graph, when (x_1 = 4), (f(4)=10); when (x_2 = 7), (f(7)=14).

Step3: Substitute the values into the formula

Substitute (x_1 = 4), (x_2 = 7), (f(x_1)=10), and (f(x_2)=14) into (\frac{f(x_2)-f(x_1)}{x_2 - x_1}). We get (\frac{14 - 10}{7-4}).

Step4: Simplify the expression

(\frac{14 - 10}{7-4}=\frac{4}{3})

Answer:

(\frac{4}{3})