Finding output level that minimizes MC

[gary_]

A firm faces the following Average Cost function
AC=1500Q^-1 + 300-27Q+1.5Q^2

Calculate the output (Q) level that minimizes:

a) Marginal Cost
b)Average Variable cost

a) AC=1500Q^-1 + 300-27Q+1.5Q^2
TC = 1500 + 300 Q -27 Q^2 + 1.5 Q^3
MC= 300 - 54 Q +4.5 Q^2

if i want to find the output that minimizes MC, do i solve for zero for this equation: MC= 300 - 54 Q +4.5 Q^2 or do i have to differentiate that equation first and then solve for zero?

 

[tkhunny]

Are you attending class? "Minimize" usually requires a derivative, unless the function is of a type where that is unnecessary (simple quadratic, for example). since you MC is a simple quadratic, you may solve it any way you like.