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

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

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FUNCTION_MANY#extreme f(x,y)=-x^2-y^2+x+2y-1

extreme points

f (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)

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