I really need help.
We let D be the half unit circle
D={(x,y)∈R^2│x^2+y^2≤1,x≥0}.
and a function f:D - R is given by f(x,y)=4xy^2-x^2
Determine the global extrema, and specify in which points of D these values is assumed.
I tried useing the method of Lagrange multipliers but does not seem to work.

Question

I really need help.
We let D be the half unit circle
D={(x,y)∈R^2│x^2+y^2≤1,x≥0}.
and a function f:D -> R is given by f(x,y)=4xy^2-x^2
Determine the global extrema, and specify in which points of D these values ​​is assumed.
I tried useing the method of Lagrange multipliers but does not seem to work.

anonymous · Answer

$$f'(x,y)=4y^2+8xy-2x=0$$
$$2y^2+4xy-x=0$$
$$x=\frac{ 2y^2}{1-4y}$$

anonymous · Answer

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