Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
cal marimum o 9:(г) — 0 %3D ng differentiable), then there uch that

cal marimum o 9:(г) — 0 %3D ng differentiable), then there uch that

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Verify the following result. Theorem. Let U be an open subset of R" and let f:U → R be a C' function Then if ro E U is either a local marimum or a local minimum of f subject to the constraints 0 = (x)*6 for i e {1,..., m} (the g, being differentiable), then there exist scalars A1,..,Am and a scalar p, not all zero, such that ( fz, (x0)\ 9kz1 (T0) (1) \Sz, (T0)/ \9kIn (T0) If the vectors 9izı (20) Fmz, (T0) \9iz, (T0), are linearly independent, it follows that an equation of the form \Imzn (T0). 9kz; (x0)) (2) \Szn (#0)/ k=1 holds. (02) "z¥6\ Hint: Use the implicit function theorem.
Transcribed Image Text:Verify the following result. Theorem. Let U be an open subset of R" and let f:U → R be a C' function Then if ro E U is either a local marimum or a local minimum of f subject to the constraints 0 = (x)*6 for i e {1,..., m} (the g, being differentiable), then there exist scalars A1,..,Am and a scalar p, not all zero, such that ( fz, (x0)\ 9kz1 (T0) (1) \Sz, (T0)/ \9kIn (T0) If the vectors 9izı (20) Fmz, (T0) \9iz, (T0), are linearly independent, it follows that an equation of the form \Imzn (T0). 9kz; (x0)) (2) \Szn (#0)/ k=1 holds. (02) "z¥6\ Hint: Use the implicit function theorem.
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS