Let $f(x,y)=x^{3}y-y^2.$

$(a)$ For what direction vec$(u)$ does $f$ decrease the fastest $at(1,1)?$

$(b)$ Find the slope $of$ the tangent line $to$ the surface $z=f(x,y)at(1,1)in$ the

direction vec$(u)=($:$1,5$:$).$

$(c)$ Find $an$ equation for the tangent line found $in$ part $(b).$

$(d)$ For what directions vec$(u)is$ the directional derivative $off(x,y)vec(u)is$ a unit vector