Use the method of Lagrange multipliers to find the absolute maximum and minimum values of f(x, y, z) = x − z subject to the constraint g(x, y, z) = x 2 + y 2 + z 2 − y = 2.

First work with stencil one. use a combination of reflections, rotations, and translations to see whether stencil one will overlap with the original pattern. list the sequence of rigid transformations you used in your attempt, noting the type of transformation, the direction, the coordinates, and the displacement