The rate of change of a function [tex] f(x) [/tex] between the interval [tex] x=a [/tex] and [tex] x=b [/tex], where [tex] b>a [/tex] , is given by
[tex] \frac{f(b)-f(a)}{b-a} [/tex] .
Here the given function is a shifted sine function. [tex] a=\frac{3\pi}{2}, b=2\pi [/tex] .
Also ,
[tex] f(\frac{3\pi}{2})=1\\ f(2\pi)=3 [/tex] .
The rate of change using the above formula is
[tex] \frac{3-1}{2\pi-\frac{3\pi}{2}}= \frac{2}{\frac{\pi}{2}}= \frac{4}{\pi} [/tex] .
The first choice is the correct choice.
