Consider the function f(x, y) = 4xy − 2x 4 − y
2 .
(a) Find the critical points of f.
(b) Use the second partials test to classify the critical
points.
(c) Show that f does not have a global minimum.
The function f(x, y) = 10−x 2−4y 2+2x has one critical point.
Find that critical point and show that it is not a saddle point.
Indicate whether this critical point is a maximum or a minimum, and
find that maximum or minimum value.