Question

C(x) = 4x2; R(x) = x3 + 5x + 10
Find all values of x for which the marginal profit is zero. Interpret your answer.

Answer 1

Assuming C(x) and R(x) are total cost/total revenue (respectively)....

Take the derivative of each to find it's slope (the change per each unit).

C'(x) = 8x R'(x) = 3x^2 + 5, or MC = 8x and MR = 3x^2+5

MP (marginal profit) = MR - MC.

MP = 3x^2 - 8x + 5. Factor that to find the roots, and set each to zero.

3x^2-5x-3x+5 = 0

x(3x-5) - 1(3x-5) = 0

(x-1) (3x-5) = 0

MP = 0 @ x = 1 and 5/3