Question

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

Answer 1

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

$\frac{f(b)-f(a)}{b-a}$ .

Here the given function is a shifted sine function. $a=\frac{3\pi}{2}, b=2\pi$ .

Also ,

$f(\frac{3\pi}{2})=1\\ f(2\pi)=3$ .

The rate of change using the above formula is

$\frac{3-1}{2\pi-\frac{3\pi}{2}}= \frac{2}{\frac{\pi}{2}}= \frac{4}{\pi}$ .

The first choice is the correct choice.

Answer 2

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