What is the extreme P(x,y)=6x^2-xy-y^2+y+8x+2 ?

The extreme P(x,y)=6x^2-xy-y^2+y+8x+2 is Saddle(-3/5 , 4/5)

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extreme P(x,y)=6x^2-xy-y^2+y+8x+2

extreme points

P (x, y) = 6 x^{2} - x y - y^{2} + y + 8 x + 2

Saddle (- \frac{3}{5}, \frac{4}{5})

Solution steps

Find the critical points:

(- \frac{3}{5}, \frac{4}{5})

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

D (x, y) = - 25

Check the sign of at each critical point

Check critical point

(- \frac{3}{5}, \frac{4}{5}) :

Saddle

Saddle (- \frac{3}{5}, \frac{4}{5})

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

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

f (x) = \frac{x ^{2} - 10 x + 25}{x - 10}

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

f (x) = \frac{x ^{5}}{20} - 4 x^{3}

What is the extreme P(x,y)=6x^2-xy-y^2+y+8x+2 ?
The extreme P(x,y)=6x^2-xy-y^2+y+8x+2 is Saddle(-3/5 , 4/5)