The cost function for production of a commodity is

C(x) =352+26x0.07x²+0.0005x³.

(a) FindC'(100). Interpret

C'(100).

This is the cost of making 100 items.This is the number of items that must be produced before the costs reach 100. This is the amount of time, in minutes, it takes to produce 100 items.This is the rate at which costs are increasing with respect to the production level whenx= 100.This is the rate at which the production level is decreasing with respect to the cost whenx= 100.

(b) Find the actual cost of producing the 101st item. (Round your answer to the nearest cent.) $