What is the extreme f(x,y)=7e^y-3ye^x ?

The extreme f(x,y)=7e^y-3ye^x is Saddle(ln(7/3),0)

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extreme f(x,y)=7e^y-3ye^x

extreme

Saddle (ln (\frac{7}{3}), 0)

Solution steps

Find the critical points:

(ln (\frac{7}{3}), 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 7 e^{y}

D (x, y) = - 21 e^{x + y} y - 9 e^{2 x}

Check the sign of at each critical point

Check critical point

(ln (\frac{7}{3}), 0) :

Saddle

Saddle (ln (\frac{7}{3}), 0)

What is the extreme f(x,y)=7e^y-3ye^x ?
The extreme f(x,y)=7e^y-3ye^x is Saddle(ln(7/3),0)