What is the extreme f(x,y)=-96*x+2*x^3+6*x*y^2-3*y^3 ?

The extreme f(x,y)=-96*x+2*x^3+6*x*y^2-3*y^3 is Saddle(12/5 , 16/5),Saddle(-12/5 ,-16/5)

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extreme f(x,y)=-96x+2x^3+6xy^2-3*y^3

extreme points

f (x, y) = - 96 \cdot x + 2 \cdot x^{3} + 6 \cdot x \cdot y^{2} - 3 \cdot y^{3}

Saddle (\frac{12}{5}, \frac{16}{5}), Saddle (- \frac{12}{5}, - \frac{16}{5})

Solution steps

Find the critical points:

(\frac{12}{5}, \frac{16}{5}), (- \frac{12}{5}, - \frac{16}{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{12}{5}, \frac{16}{5}) :

Saddle

Check critical point

(- \frac{12}{5}, - \frac{16}{5}) :

Saddle

Saddle (\frac{12}{5}, \frac{16}{5}), Saddle (- \frac{12}{5}, - \frac{16}{5})

y = x^{3} - 3 x^{2} - 9 x + 5

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

f (x, y) = \frac{x y}{( x ^{2} - y ^{2} ) ^{2}}

f (x) = 2 x^{5} - 6 x^{4}

f (x) = x^{2} - 10 x + 24

What is the extreme f(x,y)=-96*x+2*x^3+6*x*y^2-3*y^3 ?
The extreme f(x,y)=-96*x+2*x^3+6*x*y^2-3*y^3 is Saddle(12/5 , 16/5),Saddle(-12/5 ,-16/5)