$1$

$3.$ Consider the function $z=f(x,y)=10-x^2-y^4.$

$($a$)$ Sketch $f$ as a surface in $R^3.$

$($b$)$ Find the tangent plane at $x=y=1.$

$($c$)$ Sketch the level curve $z=2$ in the $xy-$plane.

$($d$)$ Find the value of the directional derivative $D_{u}f$ for $u$ parallel to $(1,1),$ and $x=2,y=1.$