Question

find maximum and minimum of x^2-xy+y^2-2x+y​

Answer 1

Answer:

So first we need to check inside the domain, I got only one point A(1,1) where f(1,1)=−3. and after further checking it is a saddle point.

Now we want to check on the edges, we have 3 edges: (1)x=y,0≤x≤y≤5 and (2)y=5,0≤x≤5 and (3)x=0,0≤y≤5.

So I started with each of them, using Lagrange. I started with the first and got:

l(x,y,λ)=x2y2−2x−2y+λ(x−y).

lx(x,y)=2xy2−2+λ=0

ly(x,y)=2x2y−2−λ=0

x−y=0→x=y.

But then what to do ? I always get x,y=1+0.5λ−−−−−−−√3.

Answer 2

Step-by-step explanation:

फाइंड द मैक्सिमा एंड मिनीमा फाइंड द मैच माय नेम ऑफ द फंक्शन एक्स स्क्वायर माइनस एक्स वाई वाई स्क्वायर माइनस टू एक्स प्लस वाई