Question

What is the rate of change between the interval x = π and x = three pi over two?

A) pi over 16
B) negative 16 over pi
C) pi over 4
D)negative 4 over pi

Answer 1

Rate of change is computed from
(rate of change) = (amount of change)/(width of interval)
= (-1 - 1)/(3π/2 - π) = -2/(π/2) = -4/π

The appropriate choice is
D) -4/π

Answer 2

Answer: Option B) negative 16 over pi

Rate of change between the interval x=a and x=b:
r=[f(b)-f(a)]/(b-a)

In this case:
a=π
b=3π/2

r=[f(3π/2)-f(π)]/(3π/2-π)

According to the graph:
f(3π/2)=-1
f(π)=7

Replacing in the formula above:
r=(-1-7)/[(3π-2π)/2]
r=(-8)/(π/2)
r=(-8)(2/π)
r=-16/π