Question

what is the average rate of change in ( f(x) ) over the interval (4,13)?

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 4\) and \(b=13\).

Step2: Find \(f(4)\) and \(f(13)\) from the graph

From the graph, when \(x = 4\), \(f(4)=8\); when \(x = 13\), \(f(13)=11\).

Step3: Substitute into the formula

Substitute \(a = 4\), \(b = 13\), \(f(4)=8\) and \(f(13)=11\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{11 - 8}{13-4}=\frac{3}{9}=\frac{1}{3}\).

Answer:

\(\frac{1}{3}\)