What is the extreme f(x,y)=5x^2y-5xy^3+4y^3 ?

The extreme f(x,y)=5x^2y-5xy^3+4y^3 is Saddle(24/25 ,(4sqrt(3))/5),Saddle(24/25 ,-(4sqrt(3))/5)

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extreme f(x,y)=5x^2y-5xy^3+4y^3

extreme points

f (x, y) = 5 x^{2} y - 5 x y^{3} + 4 y^{3}

Saddle (\frac{24}{25}, \frac{4 3}{5}), Saddle (\frac{24}{25}, - \frac{4 3}{5})

Solution steps

Find the critical points:

(\frac{24}{25}, \frac{4 3}{5}), (\frac{24}{25}, - \frac{4 3}{5})

\frac{\partial ^{2} f}{\partial x ^{2}} = 24 y - 30 x y

D (x, y) = - 225 y^{4} + 240 y^{2} - 100 x^{2}

Check the sign of at each critical point

Check critical point

(\frac{24}{25}, \frac{4 3}{5}) :

Saddle

Check critical point

(\frac{24}{25}, - \frac{4 3}{5}) :

Saddle

Saddle (\frac{24}{25}, \frac{4 3}{5}), Saddle (\frac{24}{25}, - \frac{4 3}{5})

f (x) = 12 x - 6

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

f (x) = x + \frac{16}{x} + 6, 1 \leq x \leq 32

f (x) = 3 x^{2} - 4 x + 1, 0 \leq x \leq 2

f (x) = - x^{2} - 3

What is the extreme f(x,y)=5x^2y-5xy^3+4y^3 ?
The extreme f(x,y)=5x^2y-5xy^3+4y^3 is Saddle(24/25 ,(4sqrt(3))/5),Saddle(24/25 ,-(4sqrt(3))/5)