What is the extreme f(x,y)=32y^2+x^2-x^2y ?

The extreme f(x,y)=32y^2+x^2-x^2y is Minimum(0,0),Saddle(8,1),Saddle(-8,1)

Popular >

extreme f(x,y)=32y^2+x^2-x^2y

extreme points

f (x, y) = 32 y^{2} + x^{2} - x^{2} y

Minimum (0, 0), Saddle (8, 1), Saddle (- 8, 1)

Solution steps

Find the critical points:

(0, 0), (8, 1), (- 8, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 64

D (x, y) = 64 (2 - 2 y) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(8, 1) :

Saddle

Check critical point

(- 8, 1) :

Saddle

Minimum (0, 0), Saddle (8, 1), Saddle (- 8, 1)

f (x, y) = 3 x^{2} + 6 x y + 7 y^{2} - 2 x + 4 y

f (x) = x^{\frac{1}{7}} - x^{- \frac{6}{7}}

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

f (x) = x^{\frac{1}{3}} (x^{2} - 9), - 4 \leq x \leq 2

f (x) = \frac{2 x}{x ^{2} - 25}

What is the extreme f(x,y)=32y^2+x^2-x^2y ?
The extreme f(x,y)=32y^2+x^2-x^2y is Minimum(0,0),Saddle(8,1),Saddle(-8,1)