What is the extreme f(x,y)=y-e-2x^2y ?

The extreme f(x,y)=y-e-2x^2y is Saddle(1/(sqrt(2)),0),Saddle(-1/(sqrt(2)),0)

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extreme f(x,y)=y-e-2x^2y

extreme points

f (x, y) = y - e - 2 x^{2} y

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

Solution steps

Find the critical points:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 16 x^{2}

Check the sign of at each critical point

Check critical point

(\frac{1}{2}, 0) :

Saddle

Check critical point

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

Saddle

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

f (x) = 4 x^{4} + 6 x^{3} - x

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

f (x) = 0.502994 x + 2.67066

36 x y - x^{3} - 8 y^{3}

What is the extreme f(x,y)=y-e-2x^2y ?
The extreme f(x,y)=y-e-2x^2y is Saddle(1/(sqrt(2)),0),Saddle(-1/(sqrt(2)),0)