Wyznaczyc ekstremum
: 29 maja 2007, o 12:53
Wyznaczyc ekstermum
f(x,y) = xy (1-x-y)
f(x,y) = xy (1-x-y)
\(\displaystyle{ f(x,y)=xy-x^{2}y-xy^{2}\\
\frac{\partial f}{\partial x}=y-2xy-y^{2}=0\\
\frac{\partial f}{\partial y}=x-x^{2}-2xy=0\\
x-x^{2}=y-y^{2}\\
x^{2}-y^{2}=x-y\\
(x-y)(x+y-1)=0\\
x=y\;vee\; y=-x+1}\)