What is the extreme 3x^3+2y^3-18y^2-9x+9 ?

The extreme 3x^3+2y^3-18y^2-9x+9 is Saddle(-1,6),Maximum(-1,0),Minimum(1,6),Saddle(1,0)

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extreme 3x^3+2y^3-18y^2-9x+9

extreme points

3 x^{3} + 2 y^{3} - 18 y^{2} - 9 x + 9

Saddle (- 1, 6), Maximum (- 1, 0), Minimum (1, 6), Saddle (1, 0)

Solution steps

Find the critical points:

(- 1, 6), (- 1, 0), (1, 6), (1, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 12 y - 36

D (x, y) = 18 x (12 y - 36)

Check the sign of at each critical point

Check critical point

(- 1, 6) :

Saddle

Check critical point

(- 1, 0) :

Maximum

Check critical point

(1, 6) :

Minimum

Check critical point

(1, 0) :

Saddle

Saddle (- 1, 6), Maximum (- 1, 0), Minimum (1, 6), Saddle (1, 0)

x^{4} - \frac{1}{2} x^{2} - 2

3 x^{5} - 5 x^{3} + 2

y = e^{- 4 t} + e^{- 5 t}

f (x) = \frac{2 x}{x ^{4} + 1}

f (x) = 3 x - ln (3 x), (0, 4)

What is the extreme 3x^3+2y^3-18y^2-9x+9 ?
The extreme 3x^3+2y^3-18y^2-9x+9 is Saddle(-1,6),Maximum(-1,0),Minimum(1,6),Saddle(1,0)