Problem 1. Find all the critical points of the function
f(x, y) = 2x^2 - 4xy + y^4 + 2,
say for each whether it is a local minimum, local maximum, saddle point, or
degenerate, and show how you test for this.
Please include a picture of the graph of z = f(x, y). It is fine to use an
online program for this, such as Geogebra 3D, or another of your choice.
Please label the axes on your picture, and mark and label the coordinates
of the critical points there.
Your answer.
List of critical points
Type of each (local min, local max, saddle or degenerate)
Your picture of the graph of z = f(x, y).
