Question

The total cost in Rupees is \[\text{C}(x)=0.005x^3-0.02x^2+30x+5000\]. Which expression is the marginal cost?

Options

• \[\frac{d\text{C}}{dx}=0.015x^2-0.04x+5000\]

• \[\frac{d\text{C}}{dx}=0.015x^2-0.04x+30\]

• \[\frac{d\text{C}}{dx}=0.005x^2-0.02x+30\]

• \[\frac{d\text{C}}{dx}=0.015x^3-0.04x^2+30\]

Answer 1

Marginal cost is the instantaneous rate of change of total cost with respect to output.
Differentiating gives \[\frac{d\text{C}}{dx}=0.015x^2-0.04x+30\]; the constant \[5000\] differentiates to zero.