Question

Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=4x−2y subject to the constraint x^2+2y^2=72, if such values exist

Answer 1

create the lagrange function
\[L(x,y,\lambda)=f(x,y)-\lambda(x^2+2xy^2-72)\]
use partial differntiation on \(L(x,y,\lambda)\)

Answer 2

or
\[{\partial\over\partial x}f(x,y)=\lambda{\partial\over\partial x}g(x,y)\\
{\partial\over\partial y}f(x,y)=\lambda{\partial\over\partial y}g(x,y)\\
x^2+y^2-72=0\]
use the three simultaneous equations and find the critical points.

Answer 3

okay thank you