Question

The ordering and transportation cost C for components used in a manufacturing process is approximated by the function below, where C is measured in thousands of dollars and x is the order size in

hundreds.
C(x)= 10
+
(a) Verify that C(6) - C(3).
C(6) -
C(3) =
(b) According to Rolle's theorem, the rate of change of the cost must be 0 for some order size in the Interval (3, 6). Find that order size (in components). (Round your answer to the nearest whole
number.)
Need Help?
components
Read it

Answer 1

There is no order size in the interval (3, 6) where the rate of change of the cost is 0.

Step-by-step explanation:

To verify C(6) - C(3), we need to substitute the values of x into the function C(x) = 10:

C(6) = 10(6) = 60

C(3) = 10(3) = 30

Therefore, C(6) - C(3) = 60 - 30 = 30.

According to Rolle's theorem, the rate of change of the cost must be 0 for some order size in the interval (3, 6). To find that order size, we need to find the first derivative of the function and solve for x when the derivative equals 0:

C'(x) = 10
Setting C'(x) = 0:

10 = 0

There is no solution to this equation because 10 is not equal to 0.