Suppose the cost of producing tires, t, is defined by C(t) = -0.45+2 + 12+ 450. Determine which of the following intervals has the greatest average rate of change for the cost to
produce tires.
A
Between 2 and 4 tires
B
Between 46 and 48 tires
C
Between 12 and 14 tires
D
Between 22 and 24 tires

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 =

Following this rule,

Average rate of change in the interval (2, 4)

=

=

= 9.3

Average rate of change in the interval (46, 48)

=

= -30.3

Average rate of change in the interval (12, 14)

=

= 0.3

Average rate of change in the interval (22, 24)

=

= --8.7

Average rate of change is greatest in the interval (2, 4)

Option (A) will be the answer.