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 points

f (x, y) = 7 e^{y} - 3 y e^{x}

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)

f (x, y) = (x - 4) ln (x y)

f (x) = \frac{1}{2} (7 x - 2), x \leq 3

\frac{1}{t ^{3} + 2}

f (x) = \frac{6}{7} (x^{2} - 9)^{\frac{2}{3}}

f (x, y) = 7 x y + 14 x - x^{2} + 2 y^{2}

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)