Question

If the marginal cost of a firm is f'(x) = 10 + 6x – 6x² where x is the output find the total cost assuming that the fixed cost is Rs 125.

Answer 1

Given MC = f'(x) = 10 + 6x – 6x², C = 125, TC = ? 

TC = C(x) = ∫MCdx = ∫(10 +6x – 6x²)dx = 10x + \(\frac{6x^2}{2} - \frac{6x^3}{3}\)+ C 

Total cost = 10x + 3x² – 2x³ + 125.