Marginal cost from total cost

Statement

The total cost of production is $C(q)=q^{2}+8q+50$ (in €). Find the marginal cost function and its value at $q=10$.

Solution

Marginal cost is the derivative of total cost: $MC(q)=C'(q)=2q+8.$ $MC(10)=2\cdot 10+8=\boxed{28\ \text{€}}.$