How to prove this function is quasi-convex/concave? this is the function:
$$\displaystyle f(a,b) = \frac{b^2}{4(1+a)}$$ 

For quasi convexity you have to consider for $\alpha\in R$ the set
$$\{(a,b)\in R^{2}: f(a,b)\leq \alpha\}
$$
If this set is convex for every $\alpha \in R$ you have quasi convexity.
So we obtain the equality
$$4(1+a)\leq \alpha b^{2}.$$
If you draw this set as set in $R^{2}$ for fixed $\alpha\in R$, this should give you a clue about quasi convexity...
