Marginal cost

Text

The total cost of producing $x$ units of a good is $C(x)=4x^{2}+20x+300$ (in euros). Economists call the derivative $C'(x)$ the marginal cost. Compute the marginal cost when $x=25$.

Solution

$C'(x)=8x+20$. For $x=25$: $C'(25)=200+20=220$ euros/unit. $\boxed{C'(25)=220\ \text{euros/unit}}$