{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 14-8 - Math 200 Spring 2010 Handout#16 Section 14-8...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 200, Spring 2010 Handout #16 Section 14-8 Lagrange Multipliers: Optimizing with a Constraint Theorem: Lagrange Multipliers Assume that ( ) , f x y and ( ) , g x y are differentiable functions. If ( ) , f x y has a local minimum or maximum on the constraint curve ( ) , g x y k = at ( ) , P a b = , and if ( ) , g a b ∇ ≠ , then there is a scalar λ such that ( ) ( ) , , f a b g a b λ ∇ = ∇ [The gradient vectors are parallel.] The real number λ is called the Lagrange multiplier . The vector equation is called the Lagrange condition which, equating components, yields Lagrange equations: ( ) ( ) , , x x f a b g a b λ = and ( ) ( ) , , y y f a b g a b λ = The point ( ) , P a b = is called a critical point and ( ) , f a b is called a critical value for the optimization problem. The Lagrange Multiplier Theorem is valid in any number of variables. For example, if ( ) , , f x y z has a local minimum or maximum on the constraint surface ( ) , , g x y z k = at the point ( ) , , P a b c...
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

14-8 - Math 200 Spring 2010 Handout#16 Section 14-8...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online