z=x²-xy+y²+9x-6y+20 ∂z/∂x=2x-y+9 ∂z/∂y=-x+2y-6 2x-y+9=0 -x+2y-6=0 2x-y+9=0 3y-3=0 => y=1, x=-4 ∂²z/∂x²=2=A ∂²z/∂x∂y=0=B ∂²z/∂y²=2=C Δ=AC-B²=4 > 0, A > 0 Zmin(-4;1)=16+4+1-36-6+20=-1
z=x²-xy+y²+9x-6y+20
∂z/∂x=2x-y+9
∂z/∂y=-x+2y-6
2x-y+9=0
-x+2y-6=0
2x-y+9=0
3y-3=0 => y=1, x=-4
∂²z/∂x²=2=A
∂²z/∂x∂y=0=B
∂²z/∂y²=2=C
Δ=AC-B²=4 > 0, A > 0
Zmin(-4;1)=16+4+1-36-6+20=-1