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})

a - b - 1

f (x, y) = - 4 y^{2} - 5 x^{3} + 13 x^{2}

f (x) = x \cdot e^{- \frac{x ^{2}}{8}}

f (x) = 6 x + 5 x^{- 1}

f (x) = - x^{4} + 4 x^{3} + 7

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)