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

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

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

extreme points

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

Saddle (26, - 1)

Solution steps

Find the critical points:

(26, - 1)

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

D (x, y) = - 1

Check the sign of at each critical point

Check critical point

(26, - 1) :

Saddle

Saddle (26, - 1)

f (x) = x^{3} - 6 x^{2} + 5, - 2 \leq x \leq 6

f (x) = (41000 - 5000 x) (2.5 + 0.5 x)

f (x) = - 12 x + 30

x^{3} + 15 x^{2}

f (x) = 60 x^{4} - 60 x^{3} - 60 x^{2}

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