What is the extreme f(x,y)=7(1/5 (y+sqrt(3))e^{-xy}) ?

The extreme f(x,y)=7(1/5 (y+sqrt(3))e^{-xy}) is Saddle(1/(sqrt(3)),0)

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extreme f(x,y)=7(1/5 (y+sqrt(3))e^{-xy})

extreme points

f (x, y) = 7 (\frac{1}{5} (y + 3) e^{- x y})

Saddle (\frac{1}{3}, 0)

Solution steps

Find the critical points:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{7 ( e ^{- x y} x ^{2} y + 3 e ^{- x y} x ^{2} - 2 e ^{- x y} x )}{5}

D (x, y) = \frac{98 e ^{- 2 x y} x y ^{3} + 196 3 e ^{- 2 x y} x y ^{2} - 196 e ^{- 2 x y} y ^{2} + 294 e ^{- 2 x y} x y - 196 3 e ^{- 2 x y} y - 147 e ^{- 2 x y}}{25}

Check the sign of at each critical point

Check critical point

(\frac{1}{3}, 0) :

Saddle

Saddle (\frac{1}{3}, 0)

y = 5 x^{2} - 15 x + 3

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

f (x) = 9 x^{2} - 27 x + 6

f (x) = 2 x^{3} - 24 x + 6

f (x) = \frac{16 ( x + 3 )}{x ^{4}}

What is the extreme f(x,y)=7(1/5 (y+sqrt(3))e^{-xy}) ?
The extreme f(x,y)=7(1/5 (y+sqrt(3))e^{-xy}) is Saddle(1/(sqrt(3)),0)