Find the extrema of subject to the constraint .
Using Lagrange multipliers, make a new function:
Take the partial derivatives of this function with respect to , , and .
For each equation above, find a value of lambda that works and force that value into the other two equations. Choose the other two variables appropriately to satisfy the equalities.
From 1), , and in that case . Plugging into our constraint equation yields .
From 2), , and in that case .
From 3), , and in that case .
Combining these results, the extrema are
The last two solutions may be disregarded if we are restricting to real variables.