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

The extreme f(x,y)=ye^x-2e^x-e^y+5 is Saddle(2,2)

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extreme f(x,y)=ye^x-2e^x-e^y+5

extreme points

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

Saddle (2, 2)

Solution steps

Find the critical points:

(2, 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = - e^{y}

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

Check the sign of at each critical point

Check critical point

(2, 2) :

Saddle

Saddle (2, 2)

What is the extreme f(x,y)=ye^x-2e^x-e^y+5 ?
The extreme f(x,y)=ye^x-2e^x-e^y+5 is Saddle(2,2)