Use the first and second order optimality conditions to show that x = [2.5 - 1.5 - 1]^T is a constrained

local minimum for the function

f(x) = x1^2 - 2x1 + x2^2 - x3^2 + 4x3

subject to

g(x) = x1 - x2 + 2x3 - 2 = 0.