Question

What is the rate of change from x = π to x = 3 pi over 2?

trig graph with points at 0, 0 and pi over 2, 3 and pi, 0 and 3 pi over 2, negative 3 and 2 pi, 0

negative pi over 6
negative 6 over pi
pi over 6
6 over pi

Answer 1

x goes from pi to 1.5 pi, a total of 0.5 pi. Y goes from 0 to -3. Rate of change in y over change in x. -3 over o.5 pi is -6/pi.

The answer is the second one, -6/pi.

Answer 2

Answer with explanation:

Rate of change between two points ,
`(x_(1),y_(1)) \text{and} (x_(2),y_(2))` is equal to

`=(y_(2)-y_(1))/(x_(2)-x_(1))`

We have to find rate of change from
`x=\pi \text{to} x=(3\pi)/(2)`.

Points on the curve are, (0,0) ,
`((\pi)/(2),3), (\pi,0),((3\pi)/(2),-3),\text{and}, (-2\pi ,0).`

`x_(1)=\pi ,y_(1)=0\\\\ x_(2)=(3\pi)/(2),y_(2)= -3`

Rate of change using above formula

`=(-3-0)/((3\pi)/(2)-\pi)\\\\=(-3)/((3\pi-2\pi )/(2))\\\\=(-3* 2)/(\pi)\\\\=(-6)/(\pi)`

Option B: Negative 6 over pi