Critical points, second derivative test, Taylor polynomial. Let f(x,y) = ln(1 + xy).
(a) Find and classify all critical points of f(x,y).
(b) Write down the Taylor polynomial P(x,y) at (0,0).
From your result in part (b), sketch and label the level curves of f(x,y) at (0,0).
(c) From your result in part (b), sketch the surface z = f(x,y) near (0,0).