$(3pts)$ Find the maximum and minimum values $off(x,y,z)=xy+z,$ where $(x,y,z)$ lies $on$

the sphere $of$ radius $3$ centered $at$ the origin.

$(3pts)In$ the figure below, mark the locations $of$ the minimum and maximum $off(x,y)=$

$x^2+(y-1{)}^2,$ subject $to$ the constraint $y=|x|(also$ shown$).If$ a minimum $or$ maximum does

not exist, explain why. Sketch level curves $offto$ make your determination. $Do$ NOT

perform any algebraic computations. $No$ credit will $be$ given otherwise.