Question

Find the marginal cost, marginal revenue, and marginal profit functions.
C(x) = 2x; R(x) = 5x − 0.001x2

Answer 1

marginal cost: C'(x) = 2
marginal revenue: R'(x) = 5 - 0.002x
marginal profit (call it P'): P'(x) = R'(x) - C'(x) = 3 - 0.002x

Answer 2

Find all values of x for which the marginal profit is zero. (Enter your answers as a comma-separated list.)
x =

Answer 3

Just set the marginal profit value to zero and solve for x:
0 = 3 - 0.002x
0.002x = 3
x = 1500

Answer 4

Thank you.