The cost function for production of a commodity is given below. C(x) = 352 + 21x - 0.07x2 + 0.0006x^3. C'(x) = 21 - .14x + .0018x^2.
How do I find the actual cost of producing the 101st item? I tried plugging x = 101 into C'(x), but that was wrong. Can you please show me how to find the actual cost and explain how that is different from using the derivative?