What is the extreme f(x,y)=7e^y-6ye^x ?

The extreme f(x,y)=7e^y-6ye^x is Saddle(ln(7/6),0)

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extreme f(x,y)=7e^y-6ye^x

extreme points

f (x, y) = 7 e^{y} - 6 y e^{x}

Saddle (ln (\frac{7}{6}), 0)

Solution steps

Find the critical points:

(ln (\frac{7}{6}), 0)

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

D (x, y) = - 42 e^{x + y} y - 36 e^{2 x}

Check the sign of at each critical point

Check critical point

(ln (\frac{7}{6}), 0) :

Saddle

Saddle (ln (\frac{7}{6}), 0)

f (x) = \frac{5}{x - 2}

y = x^{2} - 15 x + 54

f (x) = x^{3} - 12 x^{3}

x^{3} + 2 x^{2} + x + 1

f (x y) = 3 x^{2} - 5 x y + 2 y^{2} + 14 x + 7 y - 5

What is the extreme f(x,y)=7e^y-6ye^x ?
The extreme f(x,y)=7e^y-6ye^x is Saddle(ln(7/6),0)