What is the extreme F(x,y)=x^3-4x^2-xy-y^2 ?

The extreme F(x,y)=x^3-4x^2-xy-y^2 is Maximum(0,0),Saddle(5/2 ,-5/4)

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extreme F(x,y)=x^3-4x^2-xy-y^2

extreme points

F (x, y) = x^{3} - 4 x^{2} - x y - y^{2}

Maximum (0, 0), Saddle (\frac{5}{2}, - \frac{5}{4})

Solution steps

Find the critical points:

(0, 0), (\frac{5}{2}, - \frac{5}{4})

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

D (x, y) = - 12 x + 15

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Check critical point

(\frac{5}{2}, - \frac{5}{4}) :

Saddle

Maximum (0, 0), Saddle (\frac{5}{2}, - \frac{5}{4})

f (x) = x^{2} - 4 x - 7

f (x, y) = 4 x^{2} - 8 y^{2}

f (x) = 5 x + 4 y

x^{4} - 242 x^{2} - 2

f (x) = x (20 - 2 x) (32 - 2 x), 0 < x < 10

What is the extreme F(x,y)=x^3-4x^2-xy-y^2 ?
The extreme F(x,y)=x^3-4x^2-xy-y^2 is Maximum(0,0),Saddle(5/2 ,-5/4)