Question

Use the graph below to answer the question that follows:

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

A) 4/pi
B) pi/4
C) 2/pi
D) pi/2

Answer 1

Hey there :)

First thing you want to do is find the y intercepts of the given x's

`((3\pi )/(2) , 1)` &
`(2\pi,3)`

x1=3pi/2

y1=1

x2=2pi

y2=3

Now you are going to use the slope formula to find the average rate of change, The formula is
`(y_2-y_1)/(x_2-x_1)`

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

And now you have your answer.

`(4)/(\pi )`

Answer 2

The y value changes from y = 1 to y = 3, which is a change of 2 units. Call this P. So P = 2 = 2/1.

The x value changes from x = 3pi/2 to x = 2pi which a difference of pi/2. Call this Q. So Q = pi/2

Divide P over Q:

P/Q = (2/1) divided by (pi/2) = (2/1)*(2/pi) = 4/pi

Answer: 4/pi which is choice A