Hey! :o
We have the function $\displaystyle{y=f(x_1, x_2)=x_1\cdot x_2^2}$ and the set $M_1=\{x\in [0, \infty)^2 \mid f(x_1, x_2)>1\}$.
I want to check if the set is convex. Let $x=(x_1, x_2) , y=(y_1, y_2)\in M_1$, then $x_1\cdot x_2^2>1$ and $y_1\cdot y_2^2>1$.
We want to show that...