What is the extreme f(x,y)=(y-8)*x^2-y^2 ?

The extreme f(x,y)=(y-8)*x^2-y^2 is Maximum(0,0),Saddle(4,8),Saddle(-4,8)

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extreme f(x,y)=(y-8)*x^2-y^2

extreme points

f (x, y) = (y - 8) \cdot x^{2} - y^{2}

Maximum (0, 0), Saddle (4, 8), Saddle (- 4, 8)

Solution steps

Find the critical points:

(0, 0), (4, 8), (- 4, 8)

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

D (x, y) = - 4 (y - 8) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Check critical point

(4, 8) :

Saddle

Check critical point

(- 4, 8) :

Saddle

Maximum (0, 0), Saddle (4, 8), Saddle (- 4, 8)

y = 3 x^{3} - 36 x^{2} + 7

f (x, y) = e^{x} ln (x) y

e^{6 x} + e^{- x}

F (x, y) = 12 x^{2} + 5 x y - 17 x + 7 y - 2 y^{2} + 5

5 x y e^{- x^{2} - y^{2}}

What is the extreme f(x,y)=(y-8)*x^2-y^2 ?
The extreme f(x,y)=(y-8)*x^2-y^2 is Maximum(0,0),Saddle(4,8),Saddle(-4,8)