What is the extreme f(x,y)=-2x^3-5x^2+4xy-y^2+4y-7 ?

The extreme f(x,y)=-2x^3-5x^2+4xy-y^2+4y-7 is Saddle(-4/3 ,-2/3),Maximum(1,4)

Popular >

extreme f(x,y)=-2x^3-5x^2+4xy-y^2+4y-7

extreme points

f (x, y) = - 2 x^{3} - 5 x^{2} + 4 x y - y^{2} + 4 y - 7

Saddle (- \frac{4}{3}, - \frac{2}{3}), Maximum (1, 4)

Solution steps

Find the critical points:

(- \frac{4}{3}, - \frac{2}{3}), (1, 4)

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

D (x, y) = 24 x + 4

Check the sign of at each critical point

Check critical point

(- \frac{4}{3}, - \frac{2}{3}) :

Saddle

Check critical point

(1, 4) :

Maximum

Saddle (- \frac{4}{3}, - \frac{2}{3}), Maximum (1, 4)

f (x, y) = 5 x^{2} + 5 y^{2} + 5 x y - 10 x - 5 y + 18

f (x) = 3 x^{2} + 3 x + 1

x^{2} + x y + y^{2} - 2 x - y

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

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} - 7 x - 11 y

What is the extreme f(x,y)=-2x^3-5x^2+4xy-y^2+4y-7 ?
The extreme f(x,y)=-2x^3-5x^2+4xy-y^2+4y-7 is Saddle(-4/3 ,-2/3),Maximum(1,4)