Answer:
Option (A)
Step-by-step explanation:
Function to represent the cost of producing 't' tires is,
C(t) = -0.45t² + 12t + 450
Since average rate of change of the function in the interval (a, b) is given by,
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Following this rule,
Average rate of change in the interval (2, 4)
= [tex]\frac{C(4)-C(2)}{4-2}[/tex]
= [tex]\frac{490.8-472.2}{4-2}[/tex]
= 9.3
Average rate of change in the interval (46, 48)
= [tex]\frac{-10.8-49.8}{2}[/tex]
= -30.3
Average rate of change in the interval (12, 14)
= [tex]\frac{529.8-529.2}{2}[/tex]
= 0.3
Average rate of change in the interval (22, 24)
= [tex]\frac{478.8-496.2}{24-22}[/tex]
= --8.7
Average rate of change is greatest in the interval (2, 4)
Option (A) will be the answer.
