Answer:
[tex]\dfrac{-8}{\pi}[/tex]
Step-by-step explanation:
The rate of change of the function f(x) from point [tex]x_1[/tex] to point [tex]x_2[/tex] can be calculated using formula
[tex]\dfrac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
Given
[tex]x_1=\pi\\ \\x_2=2\pi[/tex]
From the graph of the function
[tex]f(x_1)=f(\pi)=4\\ \\f(x_2)=f(2\pi)=-4[/tex]
So, the rate of change is
[tex]\dfrac{f(x_2)-f(x_1)}{x_2-x_1}=\dfrac{-4-4}{2\pi -\pi}=\dfrac{-8}{\pi}[/tex]
