$(6$ points$)$ Suppose f$($x$,$y$)=18$x$^2-12$xy $+2/3$y$^3-48$y find the critical points and clasify local extrema

y$^3-48$y$.$ Find the critical points and classify the local extrema.

What force F$2$ will the large piston provide if the small piston is pushed down with a force F of $12\mathrm{.}0$ N$?$

If the small piston A$,$ is slowly depressed a distance of $1=0\mathrm{.}400$ m$,$ what distance y will the large piston A$2$ rise?

F$2=$

$(1)/(2)=$

N

m

What is the magnitude W of the work done when pushing down the small piston Ay$?$

What is the magnitude W$2$ of the work done when pushing up the large piston A$,?$