Question

Use the graph below to answer the question that follows:

What is the rate of change between the interval x = pi/4 and x = pi/2?

A. -8/pi

B. -pi/8

C. -32/pi

D. -pi/32

Answer 1

A.

`( - 8)/(\pi)`

Answer 2

Answer: The correct option is (C)
`-(32)/(\pi).`

Step-by-step explanation: We are given to find the rate of change between the interval
`x=(\pi)/(4)` and
`x=(\pi)/(2).`

We know that

if y = f(x) is a function of x, then the rate of change from x = a to x = b is given by

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

From the graph, we note that

`y\left((\pi)/(4)\right)=1,\\\\\\y\left((\pi)/(2)\right)=-7.`

Therefore, the rate of change between the interval
`x=(\pi)/(4)` and
`x=(\pi)/(2).` is given by

`R=(y\left((\pi)/(2)\right)-y\left((\pi)/(4)\right))/((\pi)/(2)-(\pi)/(4))\\\\\\\Rightarrow R=(-7-1)/((\pi)/(4))\\\\\\\Rightarrow R=-8* (4)/(\pi)\\\\\\\Rightarrow R=-(32)/(\pi).`

Thus, the required rate of change is
`-(32)/(\pi).`

Option (C) is CORRECT.