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Calculus: Early Transcendentals

The marginal cost function $ C^{\prime} (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.