What is the extreme f(x,y)=20xy-x^3-10y^2 ?

The extreme f(x,y)=20xy-x^3-10y^2 is Saddle(0,0),Maximum(20/3 , 20/3)

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extreme f(x,y)=20xy-x^3-10y^2

extreme points

f (x, y) = 20 x y - x^{3} - 10 y^{2}

Saddle (0, 0), Maximum (\frac{20}{3}, \frac{20}{3})

Solution steps

Find the critical points:

(0, 0), (\frac{20}{3}, \frac{20}{3})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 20

D (x, y) = 120 x - 400

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(\frac{20}{3}, \frac{20}{3}) :

Maximum

Saddle (0, 0), Maximum (\frac{20}{3}, \frac{20}{3})

f (x) = - 5 (x - 4)^{4} + 2

f (x) = x^{2} - 5

f (x, y) = x^{2} + x y + y^{2} - 25 y + 208

f (x) = x^{\frac{2}{3}}, - 1 \leq x \leq 2

f (x, y) = 5 e^{7 x y}

What is the extreme f(x,y)=20xy-x^3-10y^2 ?
The extreme f(x,y)=20xy-x^3-10y^2 is Saddle(0,0),Maximum(20/3 , 20/3)