What is the extreme f(x,y)=-294*x+2*x^3+6*x*y^2-3*y^3 ?

The extreme f(x,y)=-294*x+2*x^3+6*x*y^2-3*y^3 is Saddle(21/5 , 28/5),Saddle(-21/5 ,-28/5)

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extreme f(x,y)=-294x+2x^3+6xy^2-3*y^3

extreme points

f (x, y) = - 294 \cdot x + 2 \cdot x^{3} + 6 \cdot x \cdot y^{2} - 3 \cdot y^{3}

Saddle (\frac{21}{5}, \frac{28}{5}), Saddle (- \frac{21}{5}, - \frac{28}{5})

Solution steps

Find the critical points:

(\frac{21}{5}, \frac{28}{5}), (- \frac{21}{5}, - \frac{28}{5})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 18 y + 12 x

D (x, y) = 12 x (- 18 y + 12 x) - 144 y^{2}

Check the sign of at each critical point

Check critical point

(\frac{21}{5}, \frac{28}{5}) :

Saddle

Check critical point

(- \frac{21}{5}, - \frac{28}{5}) :

Saddle

Saddle (\frac{21}{5}, \frac{28}{5}), Saddle (- \frac{21}{5}, - \frac{28}{5})

f (x) = ln (x y - 6)

f (x) = e^{4 x} + e^{- x}

f (x, y) = 3 x^{2} + 2 y^{2} - 18 x + 16 y + 7

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

y = \frac{- 3 x}{x ^{2} + 2}

What is the extreme f(x,y)=-294*x+2*x^3+6*x*y^2-3*y^3 ?
The extreme f(x,y)=-294*x+2*x^3+6*x*y^2-3*y^3 is Saddle(21/5 , 28/5),Saddle(-21/5 ,-28/5)