If the marginal cost of manufacturing a certain item is given by Find the total cost function C(x), given that C(0) = 100.

Question

Philoid · Accepted Answer

⇒ dC = (2 + 0.15x)dx

Integrating both sides we have

⇒ ∫ dC = ∫ (2 + 0.15x)dx

⇒ ∫dC = 2∫dx + 0.15∫xdx

⇒ ……(1)

Now, given C = 100 when x = 0

⇒ 100 = 0 + 0 + k

⇒ k = 100……(2)

Putting the value of k in equation (1)