Find the points on the ellipse 2 x squared plus 3 y squared equals 1where f (x comma y )equals xyhas its extreme values.

(),(-1/2,),(-1/2,) and

()

Step-by-step explanation:

We are given that

Using Lagrange's multipliers

...(1)

...(2)

Equation (1) divided by (2)  Then we get

Substitute the values  in g(x,y)

Therefore, the points on the ellipse are

(),(-1/2,),(-1/2,) and

()

the answer will be