Use the Method of Lagrange Multipliers to Find Points on the Surface

question 229

Essay

Use the method of Lagrange multipliers to find points on the surface of $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 3$ where the function $f ( x , y , z ) = x + y + z$ has
(a) a minimum
(b) a maximum.

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