$3.($a$)$ Locate and classify the extreme points of the function $[15$ marks$]$ f$($x$,$ y$)=3$y $22$y $33$x $2+6$xy$.($b$)$ Use the method of Lagrange multipliers to find the maximum value of f$($x$,$ y$)=$ x $+$ y on the ellipse $[15$ marks$]$ x $2+13$ y $2=1.$