$1.$

Calculate both partial derivatives and evaluate them at $(1,-1)$:$f(x,y)=1000+5x-4y.$

$2.$Calculate all second order partial derivatives and evaluate them at $(-1,1)$ for $f(x,y)=1000+5x-4y.$

$3.$Your weekly cost to manufacture $x$ bicycles and $y$ tricycles is $C(x,y)=24000+60x+20y.$ Calculate and interpret both partial derivatives.

$4.$Locate and classify $($max$,$ min, saddle$)$ all critical points of $f(x,y)=4-x^2-y^2.$

$5.$Locate and classify $($max$,$ min, saddle$)$ all critical points of $g(x,y)=x^2+x+y^2-y-1.$