What is the extreme f(x)=3x^2-9x+9xy^2 ?

The extreme f(x)=3x^2-9x+9xy^2 is Saddle(0,1),Saddle(0,-1),Minimum(3/2 ,0)

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extreme f(x)=3x^2-9x+9xy^2

extreme points

f (x) = 3 x^{2} - 9 x + 9 x y^{2}

Saddle (0, 1), Saddle (0, - 1), Minimum (\frac{3}{2}, 0)

Solution steps

Find the critical points:

(0, 1), (0, - 1), (\frac{3}{2}, 0)

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

D (x, y) = 108 x - 324 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

(\frac{3}{2}, 0) :

Minimum

Saddle (0, 1), Saddle (0, - 1), Minimum (\frac{3}{2}, 0)

f (x) = \frac{x - 2}{x + 5} - 3

2 x^{4} - x^{2} + 5

f (x) = 7 x^{9} - 9 x^{7} - 5 (- 3.4)

f (x) = - 3 + x^{2} - 3 x - 3 x^{3} + 2 x^{5} + 4 x^{4}

f (x) = - x^{3} + 6 x^{2} + 135 x + 1

What is the extreme f(x)=3x^2-9x+9xy^2 ?
The extreme f(x)=3x^2-9x+9xy^2 is Saddle(0,1),Saddle(0,-1),Minimum(3/2 ,0)