What is the extreme f(x,y)=3x^{(4)}y^{(5)}+6x-7y ?

The extreme f(x,y)=3x^{(4)}y^{(5)}+6x-7y is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x,y)=3x^{(4)}y^{(5)}+6x-7y

extreme

Saddle (- \frac{7 ^{\frac{5}{8}} 2}{1 5 ^{\frac{5}{8}}}, 8 \frac{3375}{5488}), Saddle (\frac{7 ^{\frac{5}{8}} 2}{1 5 ^{\frac{5}{8}}}, - 8 \frac{3375}{5488})

Solution steps

Find the critical points:

(- \frac{7 ^{\frac{5}{8}} 2}{1 5 ^{\frac{5}{8}}}, 8 \frac{3375}{5488}), (\frac{7 ^{\frac{5}{8}} 2}{1 5 ^{\frac{5}{8}}}, - 8 \frac{3375}{5488})

\frac{\partial ^{2} f}{\partial x ^{2}} = 60 x^{4} y^{3}

D (x, y) = - 1440 x^{6} y^{8}

Check the sign of at each critical point

Check critical point

(- \frac{7 ^{\frac{5}{8}} 2}{1 5 ^{\frac{5}{8}}}, 8 \frac{3375}{5488}) :

Saddle

Check critical point

(\frac{7 ^{\frac{5}{8}} 2}{1 5 ^{\frac{5}{8}}}, - 8 \frac{3375}{5488}) :

Saddle

Saddle (- \frac{7 ^{\frac{5}{8}} 2}{1 5 ^{\frac{5}{8}}}, 8 \frac{3375}{5488}), Saddle (\frac{7 ^{\frac{5}{8}} 2}{1 5 ^{\frac{5}{8}}}, - 8 \frac{3375}{5488})

What is the extreme f(x,y)=3x^{(4)}y^{(5)}+6x-7y ?
The extreme f(x,y)=3x^{(4)}y^{(5)}+6x-7y is