5. Let $f(x,y) = x^4 + 2x^2y^2 + y^4 + 1$.
(a) Find the critical points of $f$. Does the second derivative test tell us anything here?
(b) Find and the absolute maximum and minimum of $f$ inside the circle $x^2 + y^2 = a^2$ where $a > 0$.
6. Let $D$ be the closed triangle with vertices $(2,0)$, $(0,2)$, and $(0,-2)$. Find the absolute maximum and minimum values of $f$ on $D$ where $f(x, y) = x^2 + y^2 - 2x$.
Hint: Break the boundary of the triangle into 3 line segments and look at each individually