Question

find the highest or Lowest point on the surface z=3x^4+4x^3+6y^4-16y^3+12y^2

Answer 1

Z'x=12x^3+12x^2=0=>x=0 or x=-1
Z'y=24y^3-48y^2+24y=0=>y=0 or y=1

Z(0,0)=0
Z(0,1)=2
Z(-1,0)=-1 <---Lowest
Z(-1,1)=1