Engineering Calculus Notes 375

# Engineering Calculus Notes 375 - 363 3.8. LOCAL EXTREMA 3....

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

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

Unformatted text preview: 363 3.8. LOCAL EXTREMA 3. Q(x, y ) = x2 − y 2 has A = [Q] = 10 0 −1 so ∆2 = − 1 < 0 and Q is not deﬁnite. 4. Q(x, y ) = xy has A = [Q] = 01 10 so ∆2 = − 1 < 0 and Q is not deﬁnite. 5. Finally, for the one we couldn’t decide in an obvious way: Q(x, y ) = 2x2 − 2xy + 3y 2 has A = [Q] = 2 −1 −1 3 so ∆1 = 2 > 0 ∆2 = 5 > 0 and Q is positive deﬁnite. When applied to the Hessian of f : R2 → R, the matrix representative of the Hessian form is the matrix of partials of f , sometimes called the Hessian matrix of f : → → fxx (− ) fxy (− ) a a → Hf (− ) = a → − ) f (− ) . → fxy ( a yy a this gives us 17 17 The Second Derivative Test was published by Joseph Louis Lagrange (1736-1813) in his very ﬁrst mathematical paper [33] ([20, p. 323]). ...
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