What is the extreme f(x,y)=-x^2-4x-y^2+2y-1 ?

The extreme f(x,y)=-x^2-4x-y^2+2y-1 is Maximum(-2,1)

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extreme f(x,y)=-x^2-4x-y^2+2y-1

extreme points

f (x, y) = - x^{2} - 4 x - y^{2} + 2 y - 1

Maximum (- 2, 1)

Solution steps

Find the critical points:

(- 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

(- 2, 1) :

Maximum

Maximum (- 2, 1)

f (x) = 3 x x - x^{2}

- x^{3} - x^{2}

h (x) = 2 x^{3} - 24 x

y = x x^{2} + 1

f (x) = 4 x^{2} + y^{2}

What is the extreme f(x,y)=-x^2-4x-y^2+2y-1 ?
The extreme f(x,y)=-x^2-4x-y^2+2y-1 is Maximum(-2,1)