$1.(5$ points each$)$ Determine all local extrema of the following functions. Classify each as alocal max, local min, or saddle point$($a$)$ f$($x$,$y$)=$ x$^2+2$y$^2-$ xy$+2$y$($b$)$ g$($x$,$y$)=$ x$^2+$ y$^4+2$xy