Can someone explain?

Question

The cost, in dollars, of producing x feet of track lighting is given by the following function of C(x) = 0.0003x3 − 0.002x2 + 0.1x + 2,400. What is the marginal cost, the instantaneous rate of change of the cost function, of 150 feet of track lighting?

Answer 1

Given our cost function C(x) = 0.0003x³ − 0.002x² + 0.1x + 2400, our marginal cost function will be the derivative of the original cost function, which is C'(x) = 0.0009x² - 0.004x + 0.1

The marginal cost of 150 feet of track lighting will be C'(150) = 0.0009(150)² - 0.004(150) + 0.1 = 19.75, or $19.75/ft of track lighting.

Hope this helped!