Use proper notation. Show all your work clearly. Include sentences when it helps to clarify your process. Evaluate all integrals by hand showing all the steps that lead to your answer

Give exact answers, not decimal approximations

Box-in your final answers.

The function f(x, y, z)= 2x + 2y + z under the constraint x^2 + y^2 + z^2 = 9 has both a maximum and a minimum value. Use the method of Lagrange multipliers to find both extreme values. Give your final answer in a complete sentence.