What is the extreme f(x)=288y^2+x^2-x^2y ?

The extreme f(x)=288y^2+x^2-x^2y is Minimum(0,0),Saddle(24,1),Saddle(-24,1)

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extreme f(x)=288y^2+x^2-x^2y

extreme points

f (x) = 288 y^{2} + x^{2} - x^{2} y

Minimum (0, 0), Saddle (24, 1), Saddle (- 24, 1)

Solution steps

Find the critical points:

(0, 0), (24, 1), (- 24, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 576

D (x, y) = 576 (2 - 2 y) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(24, 1) :

Saddle

Check critical point

(- 24, 1) :

Saddle

Minimum (0, 0), Saddle (24, 1), Saddle (- 24, 1)

f (x, y) = 5 x^{2} - x y + 3 y^{2}

p (b, c) = 2 b + 2 c

f (x) = ∣ x - 5 ∣ + 1

g (x) = x 8 - x^{2}

f (x, y) = 400 - 25 x^{2} - 64 y^{2}

What is the extreme f(x)=288y^2+x^2-x^2y ?
The extreme f(x)=288y^2+x^2-x^2y is Minimum(0,0),Saddle(24,1),Saddle(-24,1)