1. (10 points) Let $T$ be the triangular region in $\mathbb{R}^2$ with vertices $(-2, -2)$, $(2, 2)$, $(2, -2)$; that is, $T$ is the shaded region shown below.
$(-2, -2)$
$y$
$(2, 2)$
$(2, -2)$
Find the maximum and minimum values of $f(x, y) = x^2y - 2x^2 + 2y^2 + 5$ on $T$, as well as all points of $T$ where they are attained. Show all the steps of your reasoning.