Given C(x) = 0.005 ${\mathit{x}}^3$ – 0.02 ${\mathit{x}}^2$ + 30 x + 5000
Marginal cost is the rate of change of total cost with respect to output.
⇒ Marginal cost = $\frac{\mathit{d}\mathit{C}}{\mathit{d}\mathit{x}}$
⇒ Marginal cost = 0.005 $\left(3{\mathit{x}}^2\right)$ - 0.02 (2x) + 30 = 0.015 ${\mathit{x}}^2$ - 0.04 x + 30
Marginal cost at x 3
⇒ Marginal cost = 0.015 × $3^2$ - 0.04 × 3 + 30
⇒ Marginal cost 30.015
Therefore Marginal cost is Rs. 30.015.