What is the extreme f(x,y)=23-2x^3-y^2-6xy ?

The extreme f(x,y)=23-2x^3-y^2-6xy is Maximum(3,-9),Saddle(0,0)

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extreme f(x,y)=23-2x^3-y^2-6xy

extreme points

f (x, y) = 23 - 2 x^{3} - y^{2} - 6 x y

Maximum (3, - 9), Saddle (0, 0)

Solution steps

Find the critical points:

(3, - 9), (0, 0)

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

D (x, y) = 24 x - 36

Check the sign of at each critical point

Check critical point

(3, - 9) :

Maximum

Check critical point

(0, 0) :

Saddle

Maximum (3, - 9), Saddle (0, 0)

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

f (x) = x y + y - 11 x

3 cos^{2} (x)

f (x) = 6 x - 8 sin (x), 0 \leq x \leq π

f (x) = \frac{15 x ^{2} - 2 x - 7}{- 5 x - 1} y

What is the extreme f(x,y)=23-2x^3-y^2-6xy ?
The extreme f(x,y)=23-2x^3-y^2-6xy is Maximum(3,-9),Saddle(0,0)