Question

extreme points of z=xy subjects to the condition x+y=1 are​

Answer 1

Answer:That can’t be a necessary condition because it is not necessary that the function be differentiable.

However, using the method of Lagrange multipliers, if the function  H(x,y,z)=F(x,y,z)+λG(x,y,z)  is differentiable then you can solve  ∂F∂x+λ∂G∂x=0 , i.e.  Fx=−λGx ,

∂F∂y+λ∂G∂y=0 , i.e.  Fy=−λGy ,

∂F∂z+λ∂G∂z=0 , i.e.  Fz=−λGz ,

together with  G(x,y,z)=0 .

If you eliminate  λ  between the first two equations you should get your condition (which is clearly not sufficient as you have not used two of the equations).

Step-by-step explanation:

Answer 2

Step-by-step explanation:

the correct answer is [1/2,1/2,1/4]