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

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

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

extreme points

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

Saddle \frac{9 + 21}{5 2 3 + 21}, \frac{2 ( 3 + 21 )}{3}, Saddle - \frac{9 + 21}{5 2 3 + 21}, - \frac{2 ( 3 + 21 )}{3}

Solution steps

Find the critical points:

\frac{9 + 21}{5 2 3 + 21}, \frac{2 ( 3 + 21 )}{3}, - \frac{9 + 21}{5 2 3 + 21}, - \frac{2 ( 3 + 21 )}{3}

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

D (x, y) = - 100 x^{2} + 60 x y - 36 y^{2}

Check the sign of at each critical point

Check critical point

\frac{9 + 21}{5 2 3 + 21}, \frac{2 ( 3 + 21 )}{3} :

Saddle

Check critical point

- \frac{9 + 21}{5 2 3 + 21}, - \frac{2 ( 3 + 21 )}{3} :

Saddle

Saddle \frac{9 + 21}{5 2 3 + 21}, \frac{2 ( 3 + 21 )}{3}, Saddle - \frac{9 + 21}{5 2 3 + 21}, - \frac{2 ( 3 + 21 )}{3}

f (x) = tan (x) [- 5, 6]

- x^{3} + x^{2} + x + 8

x^{3} + y^{2} + 12 x y + 1

f (x) = 200 x - (0.003 x^{2} + 80 x + 500000)

- \frac{\frac{40}{3}}{x ^{2}} + 0.54 x

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