1:(20 Points) Consider the surfacez=x3-xyand a pointP: (1,2,0) on the surface.a:Find the maximum rate of change of the functionf(x, y) =zat pointP. Also findthe direction that has the maximum rate of change.
b:Find the equations of the tangent plane and normal line to the surface at pointP.
2:(15 Points) Consider the functionf(x, y) = (x2+y2)ex2-y2defined on the discx2+y2≤4. Find theabsolute extremas off.(Hint: Do not use Lagrange multiplier)