Question

What is the rate of change between the interval of x=3pi/2 and x=2pi<br />

4/pi<br />
Pi/4<br />
2/pi<br />
Pi/2

Answer 1

2/pi
I took the test and got it correct.

Answer 2

The rate of change of a function
`f(x)` between the interval
`x=a` and
`x=b`, where
`b>a` , is given by

`(f(b)-f(a))/(b-a)` .

Here the given function is a shifted sine function.
`a=(3\pi)/(2), b=2\pi` .

Also ,

`f((3\pi)/(2))=1\\ f(2\pi)=3` .

The rate of change using the above formula is

`(3-1)/(2\pi-(3\pi)/(2))= (2)/((\pi)/(2))= (4)/(\pi)` .

The first choice is the correct choice.