Minimizing a Quadratic

Calculus Level pending

\[ f(x, y, z) = x^2 + 2 y^2 + 3 z^2 + 2(x y + x z + y z) + 2 (x+ 2 y + 3 z) \]

Find the global minimum of the above function over \( \mathbb{R}^3 \).

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