Marginal Cost of a produc

Question

The marginal cost of a product is modeled by

dC/dx= (14)/(cuberoot(14x+7)

(a)

where x is the number of units. When x = 15, C = 140.

(b)

Find the cost function. (Round your constant term to two decimal places.)

Answer 1

dC/dx = (14)/(cuberoot(14x+7)

dC = (14)/(cuberoot(14x+7) dx

∫dC = ∫(14)/(cuberoot(14x+7) dx

C = 14∫(14x+7)^-1/3 dx

C = (14(3/2)(14x+7)^2/3)/14 + K (where K is the constant term)

C = 3/2(14x+7)^2/3 + K

Plugging in the point x = 15, C = 140 to solve for K we get:

140 = 3/2(14(15)+7)^2/3 + K

140 = 3/2(217)^2/3 + K

140 = 3/2(36.111) + K

140 = 54.1665 + K

K = 85.83

Therefore C(x) = C = 3/2(14x+7)^2/3 + 85.83