What is the extreme f(x)=x+16y^2-x^2+xy-3y^2+25 ?

The extreme f(x)=x+16y^2-x^2+xy-3y^2+25 is Saddle(26/53 ,-1/53)

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extreme f(x)=x+16y^2-x^2+xy-3y^2+25

extreme points

f (x) = x + 16 y^{2} - x^{2} + x y - 3 y^{2} + 25

Saddle (\frac{26}{53}, - \frac{1}{53})

Solution steps

Find the critical points:

(\frac{26}{53}, - \frac{1}{53})

\frac{\partial ^{2} f}{\partial x ^{2}} = 26

D (x, y) = - 53

Check the sign of at each critical point

Check critical point

(\frac{26}{53}, - \frac{1}{53}) :

Saddle

Saddle (\frac{26}{53}, - \frac{1}{53})

f (x, y) = 3 x^{2} + 3 y^{2} - 6 x + 12 y

\frac{3 x}{x ^{2} - 1}

f (x) = \frac{9 ( x ^{2} - 3 )}{x ^{3}}

y = x^{4} - 2 x^{2} + 1

f (x) = 8 sin (2 x)

What is the extreme f(x)=x+16y^2-x^2+xy-3y^2+25 ?
The extreme f(x)=x+16y^2-x^2+xy-3y^2+25 is Saddle(26/53 ,-1/53)