What is the extreme f(x)=9-2x+4y-x^2-2y^3 ?

The extreme f(x)=9-2x+4y-x^2-2y^3 is

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extreme f(x)=9-2x+4y-x^2-2y^3

extreme points

f (x) = 9 - 2 x + 4 y - x^{2} - 2 y^{3}

Maximum (- 1, \frac{2}{3}), Saddle (- 1, - \frac{2}{3}), Saddle (- 1, - \frac{2}{3}), Maximum (- 1, \frac{2}{3})

Solution steps

Find the critical points:

(- 1, \frac{2}{3}), (- 1, - \frac{2}{3}), (- 1, - \frac{2}{3}), (- 1, \frac{2}{3})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 12 y

D (x, y) = 24 y

Check the sign of at each critical point

Check critical point

(- 1, \frac{2}{3}) :

Maximum

Check critical point

(- 1, - \frac{2}{3}) :

Saddle

Check critical point

(- 1, - \frac{2}{3}) :

Saddle

Check critical point

(- 1, \frac{2}{3}) :

Maximum

Maximum (- 1, \frac{2}{3}), Saddle (- 1, - \frac{2}{3}), Saddle (- 1, - \frac{2}{3}), Maximum (- 1, \frac{2}{3})

y = x (6 - 2 x)^{2}

\frac{x + 2}{x ^{3}}

f (x) = - 0.03 x^{2} + 300 x - 100000

f (x) = x^{\frac{1}{3}} (x - 4), - 125 \leq x \leq 125

x (16 - 2 x)

What is the extreme f(x)=9-2x+4y-x^2-2y^3 ?
The extreme f(x)=9-2x+4y-x^2-2y^3 is