What is the extreme-x^4y^2-x^4+2x^3y+2x^2y+x^2-2x-2 ?

The extreme-x^4y^2-x^4+2x^3y+2x^2y+x^2-2x-2 is Maximum(1,2),Maximum(-1,0)

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extreme-x^4y^2-x^4+2x^3y+2x^2y+x^2-2x-2

extreme points

- x^{4} y^{2} - x^{4} + 2 x^{3} y + 2 x^{2} y + x^{2} - 2 x - 2

Maximum (1, 2), Maximum (- 1, 0)

Solution steps

Find the critical points:

(1, 2), (- 1, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 2 x^{4}

D (x, y) = - 40 x^{6} y^{2} + 24 x^{6} + 72 x^{5} y + 56 x^{4} y - 40 x^{4} - 48 x^{3} - 16 x^{2}

Check the sign of at each critical point

Check critical point

(1, 2) :

Maximum

Check critical point

(- 1, 0) :

Maximum

Maximum (1, 2), Maximum (- 1, 0)

f (x \cdot y) = x y + 8^{x y}

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

f (t) = \frac{x}{x + 25} [0.9]

f (x) = - x^{3} + 3 x^{2} + 429 x + 5242

f (t) = 108 t - t^{3}

What is the extreme-x^4y^2-x^4+2x^3y+2x^2y+x^2-2x-2 ?
The extreme-x^4y^2-x^4+2x^3y+2x^2y+x^2-2x-2 is Maximum(1,2),Maximum(-1,0)