Chapter 8.4, Problem 1E

The marginal cost function C′(x) was defined to be the derivative of the cost function. (See Sections 3.7 and 4.7.) The marginal cost of producing x gallons of orange juice is

$C^{\prime }(x)=0.82-0.00003x+0.000000003x^2$

(measured in dollars per gallon). The fixed start-up cost is C(0) = $ 18,000. Use the Net Change Theorem to find the cost of producing the first 4000 gallons of juice.