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

The extreme f(x,y)=2x^4+5xy^2+y+2 is Saddle(-(\sqrt[5]{625})/(10), 1/(\sqrt[5]{625)})

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

extreme points

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

Solution steps

Find the critical points:

\frac{\partial ^{2} f}{\partial x ^{2}} = 10 x

D (x, y) = 240 x^{3} - 100 y^{2}

Check the sign of at each critical point

Check critical point

Saddle

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

ln (x - y) + x^{2} + y

f (x) = x^{101} + x^{51} + x + 1

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

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

What is the extreme f(x,y)=2x^4+5xy^2+y+2 ?
The extreme f(x,y)=2x^4+5xy^2+y+2 is Saddle(-(\sqrt[5]{625})/(10), 1/(\sqrt[5]{625)})