Study guide and 5 practice problems on:

## Lagrange multipliers

Lagrange multipliers are a convenient tool to solve constrained minimization problems.
To use Lagrange multipliers to solve the problem $$\min f(x,y,z) \text{ subject to } g(x,y,z) = 0,$$

1. Form the augmented function $$L(x,y,z,\lambda) = f(x,y,z) - \lambda g(x,y,z)$$

2. Set all partial derivatives of $L$ equal to zero

3. Solve for $x,y,z$.

Lagrange multipliers also work when solving a constrained maximization problem.