Engineering Calculus Notes 350

Engineering Calculus Notes 350 - 338 CHAPTER 3. REAL-VALUED...

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: 338 CHAPTER 3. REAL-VALUED FUNCTIONS: DIFFERENTIATION We can solve the first three equations for λ2 and eliminate it: (1 − λ1 )x = (1 − λ1 )y = 2z. The first of these equations says that either λ1 = 1 or x = y. If λ1 = 1, then the second equality says that z = 0, so y = 1 − x. In this case the first constraint gives us x2 + (1 − x)2 = 4 2x2 − 2x − 3 = 0 √ 1 x = (1 ± 7) 2 √ 1 y = (1 ∓ 7) 2 yielding two relative critical points, at which the function f has value f √1 √ 1 (1 ± 7), (1 ∓ 7), 0 2 2 = 9 . 4 If x = y , then the first constraint tells us x2 + x2 = 4 √ x=y=± 2 and then the second constraint says z = 1 − 2x √ =1∓2 2 ...
View Full Document

This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

Ask a homework question - tutors are online