Check that the function:
f(x1, x2, x3) = (x1)^2 + (x2)^2 + (x3)^2 - x1 - x2 - x3
is convex. Find the extreme values of f under the conditions:
(x1)^2 + (x2)^2 = 4, -1 <= x3 <= 1. (x3 goes from -1 to 1)
This provides an example of checking that a function is convex and finding extreme values.