What is the extreme f(x)=-3x^2y-84xy+7y^2 ?

The extreme f(x)=-3x^2y-84xy+7y^2 is Saddle(-28,0),Saddle(0,0),Minimum(-14,-42)

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extreme f(x)=-3x^2y-84xy+7y^2

extreme points

f (x) = - 3 x^{2} y - 84 x y + 7 y^{2}

Saddle (- 28, 0), Saddle (0, 0), Minimum (- 14, - 42)

Solution steps

Find the critical points:

(- 28, 0), (0, 0), (- 14, - 42)

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

D (x, y) = - 84 y - 36 x^{2} - 1008 x - 7056

Check the sign of at each critical point

Check critical point

(- 28, 0) :

Saddle

Check critical point

(0, 0) :

Saddle

Check critical point

(- 14, - 42) :

Minimum

Saddle (- 28, 0), Saddle (0, 0), Minimum (- 14, - 42)

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

0.5 x^{2} + 15 x + 5000

f (x) = x^{3} - x - 1

f (x) = \frac{2 x ^{2} + 6}{x - 1}

f (x) = x^{5} + 32

What is the extreme f(x)=-3x^2y-84xy+7y^2 ?
The extreme f(x)=-3x^2y-84xy+7y^2 is Saddle(-28,0),Saddle(0,0),Minimum(-14,-42)