What is the extreme w(x,y)=xy+(e^y)/(y^2+1) ?

The extreme w(x,y)=xy+(e^y)/(y^2+1) is Saddle(-1,0)

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extreme w(x,y)=xy+(e^y)/(y^2+1)

extreme points

w (x, y) = x y + \frac{e ^{y}}{y ^{2} + 1}

Saddle (- 1, 0)

Solution steps

Find the critical points:

(- 1, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{e ^{y} ( y - 1 ) ( y ^{3} - 3 y ^{2} + 5 y + 1 )}{( y ^{2} + 1 ) ^{3}}

D (x, y) = - 1

Check the sign of at each critical point

Check critical point

(- 1, 0) :

Saddle

Saddle (- 1, 0)

f (x) = x^{8} + \frac{8}{x}

f (x, y) = 9 - x^{2} - 4 - y^{2}

f (x) = x x + 9

f (x) = 6 x^{\frac{2}{3}} - 4 x

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

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