What is the extreme R(x,y)=-x^2-y^2+x+2y-1 ?

The extreme R(x,y)=-x^2-y^2+x+2y-1 is Maximum(1/2 ,1)

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extreme R(x,y)=-x^2-y^2+x+2y-1

extreme points

R (x, y) = - x^{2} - y^{2} + x + 2 y - 1

Maximum (\frac{1}{2}, 1)

Solution steps

Find the critical points:

(\frac{1}{2}, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 2

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(\frac{1}{2}, 1) :

Maximum

Maximum (\frac{1}{2}, 1)

f (x) = 9 x^{3} - 7 x^{2} + 3 x + 10

f (x, y) = (2 x - x^{2}) (2 y - y^{2})

x^{2} - 6 x + 10

f (x, y) = 7 - x y + x^{5} y^{3}

f (x) = 2 x^{3} - 3 x^{2} - 12 x + 8

What is the extreme R(x,y)=-x^2-y^2+x+2y-1 ?
The extreme R(x,y)=-x^2-y^2+x+2y-1 is Maximum(1/2 ,1)