What is the extreme x^2-6x+3y^3-y+8 ?

The extreme x^2-6x+3y^3-y+8 is Minimum(3, 1/3),Saddle(3,-1/3)

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extreme x^2-6x+3y^3-y+8

extreme points

x^{2} - 6 x + 3 y^{3} - y + 8

Minimum (3, \frac{1}{3}), Saddle (3, - \frac{1}{3})

Solution steps

Find the critical points:

(3, \frac{1}{3}), (3, - \frac{1}{3})

\frac{\partial ^{2} f}{\partial x ^{2}} = 18 y

D (x, y) = 36 y

Check the sign of at each critical point

Check critical point

(3, \frac{1}{3}) :

Minimum

Check critical point

(3, - \frac{1}{3}) :

Saddle

Minimum (3, \frac{1}{3}), Saddle (3, - \frac{1}{3})

f (x, y) = 3 x^{2} + 4 x y + y^{2} + x^{3}

- sin (2 x)

f (x) = - 2 x^{3} + 42 x^{2} - 270 x + 3

f (x) = - 2 x^{3} + 42 x^{2} - 270 x + 8

x^{4} - y^{4} - 2 x^{2} + 2 y^{2}

What is the extreme x^2-6x+3y^3-y+8 ?
The extreme x^2-6x+3y^3-y+8 is Minimum(3, 1/3),Saddle(3,-1/3)