What is the extreme f(x)=50y^2+x^2-x^2y ?

The extreme f(x)=50y^2+x^2-x^2y is Minimum(0,0),Saddle(10,1),Saddle(-10,1)

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extreme f(x)=50y^2+x^2-x^2y

extreme points

f (x) = 50 y^{2} + x^{2} - x^{2} y

Minimum (0, 0), Saddle (10, 1), Saddle (- 10, 1)

Solution steps

Find the critical points:

(0, 0), (10, 1), (- 10, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 100

D (x, y) = 100 (2 - 2 y) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(10, 1) :

Saddle

Check critical point

(- 10, 1) :

Saddle

Minimum (0, 0), Saddle (10, 1), Saddle (- 10, 1)

f (x) = 8 x^{\frac{3}{4}} - x, 0 \leq x \leq 4096

\frac{x ^{2} - 7}{x + 4}

f (x) = \frac{x ^{3}}{3} + 4 x^{2} + 15 x + 7

T (x, y) = \frac{x ^{3} + y ^{3}}{( x + y ) ^{2} - 3 x y} - x

What is the extreme f(x)=50y^2+x^2-x^2y ?
The extreme f(x)=50y^2+x^2-x^2y is Minimum(0,0),Saddle(10,1),Saddle(-10,1)