Optimization for minimum cost, with the total cost function $C=TQ^{1/a} + F$ I have the function $C=TQ^{1/a} + F$. Where C is total cost, Q is output, a is a positive parametric constant, F is fixed cost, and T measures the technology available to the firm (Parameter). We also know that $T > 0$.
A hint is to use calculus of optimization, and to check our second-order condition.
I got the answer of it being convex with the function of $T(1/a)(1/a-1)Q^{1/a-2}$
However I can't figure out the rest:
Assuming $a<0.5$, and by using optimization what is the value of q that minimizes the average cost?
Hint: the answer for $q$ will be in the parameters of the model, be sure to check the second order condition.

a) Look up what it means to be concave/convex. Sketch a graph of C. Based on the graph, does it look like C is concave/convex? How might you prove it?
b) What is the definition of "average cost"? Now this is a standard calc 1 exercise: Find the global minimum of the average cost.
