What is the extreme f(x,y)=5x^4-x^2+3y^2 ?

The extreme f(x,y)=5x^4-x^2+3y^2 is Saddle(0,0),Minimum(-1/(sqrt(10)),0),Minimum(1/(sqrt(10)),0)

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extreme f(x,y)=5x^4-x^2+3y^2

extreme points

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

Saddle (0, 0), Minimum (- \frac{1}{10}, 0), Minimum (\frac{1}{10}, 0)

Solution steps

Find the critical points:

(0, 0), (- \frac{1}{10}, 0), (\frac{1}{10}, 0)

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

D (x, y) = 6 (60 x^{2} - 2)

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(- \frac{1}{10}, 0) :

Minimum

Check critical point

(\frac{1}{10}, 0) :

Minimum

Saddle (0, 0), Minimum (- \frac{1}{10}, 0), Minimum (\frac{1}{10}, 0)

x + 2 + 1

y e^{x^{2} - 2 y^{2}}

f (x) = 2 - 2 cos (x), (0, 2 π)

\frac{d}{d o} (2 x + 1 o n [0.2])

f (x) = \frac{( x ^{2} - 5 ) ^{3}}{125}

What is the extreme f(x,y)=5x^4-x^2+3y^2 ?
The extreme f(x,y)=5x^4-x^2+3y^2 is Saddle(0,0),Minimum(-1/(sqrt(10)),0),Minimum(1/(sqrt(10)),0)