What is the extreme f(x,y)=x^2*y^2+x^2-x*y^2-5*x-7 ?

The extreme f(x,y)=x^2*y^2+x^2-x*y^2-5*x-7 is Minimum(5/2 ,0),Saddle(1,sqrt(3)),Saddle(1,-sqrt(3))

Popular >

extreme f(x,y)=x^2y^2+x^2-xy^2-5*x-7

extreme points

f (x, y) = x^{2} \cdot y^{2} + x^{2} - x \cdot y^{2} - 5 \cdot x - 7

Minimum (\frac{5}{2}, 0), Saddle (1, 3), Saddle (1, - 3)

Solution steps

Find the critical points:

(\frac{5}{2}, 0), (1, 3), (1, - 3)

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

D (x, y) = - 12 x^{2} y^{2} + 4 x^{2} + 12 x y^{2} - 4 x - 4 y^{2}

Check the sign of at each critical point

Check critical point

(\frac{5}{2}, 0) :

Minimum

Check critical point

(1, 3) :

Saddle

Check critical point

(1, - 3) :

Saddle

Minimum (\frac{5}{2}, 0), Saddle (1, 3), Saddle (1, - 3)

\frac{3 x}{x - 2}

f (x, y) = 8 x y + \frac{1}{x} + \frac{1}{y}

f (x, y) = 3 x y - 6 x - 3 y + 7

5 + 6 x - 8 x^{3}

y = (t - 3 t^{2})^{\frac{1}{3}}

What is the extreme f(x,y)=x^2*y^2+x^2-x*y^2-5*x-7 ?
The extreme f(x,y)=x^2*y^2+x^2-x*y^2-5*x-7 is Minimum(5/2 ,0),Saddle(1,sqrt(3)),Saddle(1,-sqrt(3))