b$)(6$ pts$)$ For each function below, determine whether $(0,0)$ corresponds to a local max, a local min, or a saddle point. You must justify your answer to receive full credit.

I. $g(x,y)=x^4{y}^2$

II$.h(x,y)=x^2{y}^2-4$

III. $r(x,y)=x^2{y}^3$