a) Let C(r) be the cost of a car as a function of the interest rate at which it is sold. You can assume that C is a monotonic function and it has an inverse. Express into a single mathematical formula the statement:

"When the cost of a car is 20 thousand dollars, in order to reduce the total cost by one thousand dollars, we estimate that the interest rate has to decrease by 0.5."

Explain your reasoning in detail

b) Given C(3.5) = 35000 and C' (3.5) = 1/10000, estimate which interest rate will be charged for a car costing $32000.

c) Assume that C(3.5) = 35000, C 0 (3.5) = 1/10000, and C 00(3.5) = 1/20000. Estimate C(4) and C' (4).