What is the extreme x^3+3xy^2-3x ?

The extreme x^3+3xy^2-3x is Saddle(0,1),Saddle(0,-1),Minimum(1,0),Maximum(-1,0)

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extreme x^3+3xy^2-3x

extreme points

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

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

Solution steps

Find the critical points:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = 6 x

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

Check the sign of at each critical point

Check critical point

(0, 1) :

Saddle

Check critical point

(0, - 1) :

Saddle

Check critical point

(1, 0) :

Minimum

Check critical point

(- 1, 0) :

Maximum

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

f (x) = x^{\frac{2}{3}} (x - 2), - 2 \leq x \leq 2

f (x) = x^{2} - 2 x - lo g_{3} (y)

f (x) = 7 - (y) e^{- 0.45 x}

f (x) = x^{3} - 36 x^{2}, - 12 \leq x \leq 36

f (x) = (6 - 2 x) (3 - 2 x) x

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