What is the extreme f(x,y)=-x^2+2xy-7y^2+2x+10y+8 ?

The extreme f(x,y)=-x^2+2xy-7y^2+2x+10y+8 is Maximum(2,1)

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extreme f(x,y)=-x^2+2xy-7y^2+2x+10y+8

extreme points

f (x, y) = - x^{2} + 2 x y - 7 y^{2} + 2 x + 10 y + 8

Maximum (2, 1)

Solution steps

Find the critical points:

(2, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 14

D (x, y) = 24

Check the sign of at each critical point

Check critical point

(2, 1) :

Maximum

Maximum (2, 1)

f (x) = 2 x e^{x} - 4 x^{3}

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

f (x) = 18500 (0.25 - r^{2})

f (x) = - x^{2} + 8 x - 15, 3 \leq x \leq 5

f (x) = - 2 x^{2} - 2 y^{2} + 20 x + 16 y - 4

What is the extreme f(x,y)=-x^2+2xy-7y^2+2x+10y+8 ?
The extreme f(x,y)=-x^2+2xy-7y^2+2x+10y+8 is Maximum(2,1)