Question

A manufacturer has found that marginal costs are 3𝑞 2 − 60𝑞 + 400 dollars per unit when q units have been produced. The total costs of producing the first 2 units are $ 900. What is the total cost of producing the first 5 units?

Answer 1

$C\left( q \right) =\int{\left( 3q^2-60q+400 \right) dq}=q^3-30q^2+400q+C\\C\left( 2 \right) =900\Rightarrow 2^3-30\cdot 2^2+400\cdot 2+C=900\Rightarrow \\\Rightarrow C=212\\C\left( q \right) =q^3-30q^2+400q+212\\C\left( 5 \right) =5^3-30\cdot 5^2+400\cdot 5+212=1587$