What is the extreme (x^2y)/2-x^2+xy-2x-y^2 ?

The extreme (x^2y)/2-x^2+xy-2x-y^2 is Saddle(2,2),Saddle(-4,2),Maximum(-1,-1/4)

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extreme (x^2y)/2-x^2+xy-2x-y^2

extreme points

\frac{x ^{2} y}{2} - x^{2} + x y - 2 x - y^{2}

Saddle (2, 2), Saddle (- 4, 2), Maximum (- 1, - \frac{1}{4})

Solution steps

Find the critical points:

(2, 2), (- 4, 2), (- 1, - \frac{1}{4})

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

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

Check the sign of at each critical point

Check critical point

(2, 2) :

Saddle

Check critical point

(- 4, 2) :

Saddle

Check critical point

(- 1, - \frac{1}{4}) :

Maximum

Saddle (2, 2), Saddle (- 4, 2), Maximum (- 1, - \frac{1}{4})

y = x^{2} - 2 x

f (x) = 2 x^{3} - 3 x^{2} - 12 x + 5, 0 \leq x \leq 3

- x^{2} + 3 x - 2, 1 \leq x \leq 3

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

f (x) = x^{2}, - 2 \leq x \leq 1

What is the extreme (x^2y)/2-x^2+xy-2x-y^2 ?
The extreme (x^2y)/2-x^2+xy-2x-y^2 is Saddle(2,2),Saddle(-4,2),Maximum(-1,-1/4)