# CoV2

From Example Problems

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 .

1)

2)

3)

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.