What is the extreme f(x)=x^2y^2+x^2y+x ?

The extreme f(x)=x^2y^2+x^2y+x is Saddle(2,-1/2)

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extreme f(x)=x^2y^2+x^2y+x

extreme points

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

Saddle (2, - \frac{1}{2})

Solution steps

Find the critical points:

(2, - \frac{1}{2})

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

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

Check the sign of at each critical point

Check critical point

(2, - \frac{1}{2}) :

Saddle

Saddle (2, - \frac{1}{2})

f (t) = t u (t - 2)

f (x) = x^{3} - 5 x^{2} - 8 x

f (x, y) = - 2 y - 3 x + 6

f (x) = \frac{( x - 2 ) ^{2}}{x + 6}

f (x) = cot (x) + tan (x)

What is the extreme f(x)=x^2y^2+x^2y+x ?
The extreme f(x)=x^2y^2+x^2y+x is Saddle(2,-1/2)