Tricky Calc Problem

Question

A juice company has found that the marginal cost of producing x pints of fresh-squeezed orange juice is given by the function below, where C'(x) is in dollars. Approximate the total cost of producing 258 pt of juice, using 3 subintervals over [0,258] and the left endpoint of each subinterval.

C'(x)=0.000007x^2 - 0.0035x + 5, for x <= 350

Answer 1

Total cost is the integral of marginal cost

C(x) = .000007x^3/3 -0035x^2/2 +5x

let x=258, plug into the C(x) equation

That's 258 cubed, times .000007, divided by 3, all minus .0035/2 times 258 squared + 5 times 258

Just use a calculator and calculate. Whatever you get should be close to your approximation

dividing it up into 3 intervals. But since you're using the left end point, that approximation should be less than the real answer.