2. Consider the problem
max $f(x, y, z) = 4z - x^2 - y^2 - z^2$
subject to $g(x, y, z) = z - xy = 0$
[*]
a. Use Lagrange's method to find necessary conditions for the solution of
the problem, and find all triples $(x, y, z)$ that satisfy these conditions.
b. The point $(1, 1, 1)$ is a maximum point in [*]. Find an approximate value
for the change in the maximum value of $f$ if we change the constraint
from $z - xy = 0$ to $z - xy = 0.1$.
