c(q)=60q-12q^2+q^3. At level of output is average cost minimum?

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The average cost AC is `AC(q)=c(q)/q=60-12q+q^2.`

It is a quadratic equation, its graph is a upward parabola since the coefficient of q^2 is positive.

The critical point is a minimum.

`AC'(q)=-12+2q`

`AC'(q)=0` iff `q=6`

 

The average cost is minimum at the level q=6

 

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