What is the extreme f(x)=5ye^x-6e^y ?

The extreme f(x)=5ye^x-6e^y is Saddle(ln(6/5),0)

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extreme f(x)=5ye^x-6e^y

extreme points

f (x) = 5 y e^{x} - 6 e^{y}

Saddle (ln (\frac{6}{5}), 0)

Solution steps

Find the critical points:

(ln (\frac{6}{5}), 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 6 e^{y}

D (x, y) = - 30 e^{x + y} y - 25 e^{2 x}

Check the sign of at each critical point

Check critical point

(ln (\frac{6}{5}), 0) :

Saddle

Saddle (ln (\frac{6}{5}), 0)

f (x) = x_{2} - 4 \cdot 2 - 4 x

f (x) = x^{2} - 9 ln (x)

f (x) = (\frac{1}{12} x^{3} + x^{2} + 3 x + \frac{26}{3})

f (x) = - 5 x^{3} + 45 x

f (x) = - 0.020724 x^{2} + 0.3692 x - 0.6287

What is the extreme f(x)=5ye^x-6e^y ?
The extreme f(x)=5ye^x-6e^y is Saddle(ln(6/5),0)