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Suppose an extremal value of f occurs when x = x*, y = y*, 1 = X* (we'll call (x*, y*, A*) an extremal point). Define a new function, L(x, y, A, c) = f(x, y) – A(g(x, y) – c). Calculate the vector VL(x*, y*, X*, c) = (Lx, Ly, Lx, Lc)x=r*,y=y*,A=A* •

Suppose an extremal value of f occurs when x = x*, y = y*, 1 = X* (we'll call (x*, y*, A*) an extremal point). Define a new function, L(x, y, A, c) = f(x, y) – A(g(x, y) – c). Calculate the vector VL(x*, y*, X*, c) = (Lx, Ly, Lx, Lc)x=r*,y=y*,A=A* •

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
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I want you to derive a meaning for the "multiplier" A. In what follows, we consider the problem of finding an extremal(maximal or minimal) value of f(x.y) subject to the constraint equation g(x,y),and the constraint g(x.y) =c. = x*, y = y*, ) = \* (we'll call Suppose an extremal value of f occurs when x = (x*, y*, A*) an extremal point). Define a new function, L(x, y, A, c) = f(x, y) – A(g(x, y) – c). %3D | Calculate the vector VL(x*, y*, X*, c) = (Lz, Ly, Lx, L=r'y=y*,A=x• ·
Transcribed Image Text:I want you to derive a meaning for the "multiplier" A. In what follows, we consider the problem of finding an extremal(maximal or minimal) value of f(x.y) subject to the constraint equation g(x,y),and the constraint g(x.y) =c. = x*, y = y*, ) = \* (we'll call Suppose an extremal value of f occurs when x = (x*, y*, A*) an extremal point). Define a new function, L(x, y, A, c) = f(x, y) – A(g(x, y) – c). %3D | Calculate the vector VL(x*, y*, X*, c) = (Lz, Ly, Lx, L=r'y=y*,A=x• ·
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