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

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

extreme points

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

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})

f (x) = 5 x^{5} - 75 x^{3}

\frac{4 x}{x ^{2} + 4}

f (x) = - 0.018 x^{3} + 0.215 x^{2} + 0.057 x + 1

f (x) = 2 x^{3} + 9 x^{2} - 60 x + 7, - 5 \leq x \leq 5

f (x) = x^{3} + 4 x^{2} + 4 x

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