Originally Posted by
Miss
Find the max&min of the following function :
$\displaystyle f(x,y,z)=8xy-3y^2+32z+5$
subject to the constraint : $\displaystyle 4x^2+y^2+4z^2=24$
By the Lagrang Multipliers' method :
$\displaystyle 8y=\lambda 8x$........(1)
$\displaystyle 8x-6y=\lambda 2y$.......(2)
$\displaystyle 32=\lambda 8z$.......(3)
$\displaystyle 4x^2+y^2+4z^2=24$
(1) will be : $\displaystyle y=\lambda x$
(2) will be : $\displaystyle 4x-3y=\lambda y$
(3) will be : $\displaystyle 4=\lambda z$
then ?!!