Find Total Cost Given Company's Marginal Cost Function

Question

A company's marginal cost function is  where x is the number of units. Find the total cost of the first 49 units (from x=0 to x=49)

Total cost: 

Answer 1

Hello Rachel,

Marginal Cost is the cost to produce each unit, and we want to find the total cost of producing the first 49 units. Generally speaking, if the cost function is represented by C(x), the marginal cost function is the derivative, C'(x). Therefore, if we want to find the total cost function from the marginal cost function we need to integrate. And since we are looking specifically at the total cost to produce the first 49 units, we need a definite integral:

∫₀⁴⁹ 17√x dx = 17*x^3/2*2/3 ₀⁴⁹]

= 34/3 *(49)^3/2-0

= 34/3 *343

= 11,662/3