Average cost function and marginal cost function proof

Question

I was wondering if someone could help me prove the following.

Let $A(Q)$ be an average cost function and $M(Q)$ the corresponding marginal cost function. Show that if $M(Q)>A(Q)>0$ then $A(Q)$ is strictly increasing.

Answer 1

If you consider the marginal cost as the derivative of total cost, then $M(Q)>0$ means the cost is increasing. Because $M(Q)>A(Q)$, the marginal increase in cost is greater than the current average. Hence the average will increase as well.

Sorry if this isn't the 'mathematical' explanation you're looking for.