marginal cost

Question

The marginal cost of producing the xth item is given by (-x+10)^2

 

Find the total cost function, C, assuming the total cost is zero if no items are produced.

 

C(x)=?

 

Answer 1

Margnal cost = C'(x) = (-x+10)²  

 

C(x) = ∫C'(x)dx = ∫(-x+10)²dx      Let u = -x+10

                                                    Then, du = -dx    So, dx = -du

 

C(x) = -∫u²du

 

        = -(1/3)u³ + K

 

        = -(1/3)(-x+10)³ + K

 

Since C(0) = 0, we have -(1/3)(1000) + K = 0

 

                                                           K = (1/3)(1000)

 

So, C(x) = (-1/3)[(-x+10)³ - 1000]