Find all constrained relative extrema of f(x, y, z) = (x − 1)^2 + (y − 1)^2 + z^2 subjected the constraint 2x − 3y + z = 19. If you get only one constrained relative extremum, then decide if it is a constrained relative maximum or a constrained relative minimum. Justify your answer.

Find all constrained relative extrema of f(x, y, z) = (x − 1)^2 + (y − 1)^2 + z^2
subjected the constraint 2x − 3y + z = 19. If you get only one constrained relative
extremum, then decide if it is a constrained relative maximum or a constrained
relative minimum. Justify your answer.