What is the extreme 6xy-x^2y-xy^2 ?

The extreme 6xy-x^2y-xy^2 is Saddle(0,6),Maximum(2,2)

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extreme 6xy-x^2y-xy^2

extreme points

6 x y - x^{2} y - x y^{2}

Saddle (0, 6), Maximum (2, 2)

Solution steps

Find the critical points:

(0, 6), (2, 2)

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

D (x, y) = - 4 x y + 24 x - 4 x^{2} + 24 y - 4 y^{2} - 36

Check the sign of at each critical point

Check critical point

(0, 6) :

Saddle

Check critical point

(2, 2) :

Maximum

Saddle (0, 6), Maximum (2, 2)

f (x) = 2 x^{3} - 3 x^{2} - 72 x + 9, - 4 \leq x \leq 5

f (x) = - 3 x^{2} + 42 x - 141

f (x) = x^{2} + 9 x - 2

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

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

What is the extreme 6xy-x^2y-xy^2 ?
The extreme 6xy-x^2y-xy^2 is Saddle(0,6),Maximum(2,2)