What is the extreme f(x,y)=-x^3+4xy-2y^2+4x+1 ?

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

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extreme f(x,y)=-x^3+4xy-2y^2+4x+1

extreme

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

Solution steps

Find the critical points:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = - 4

D (x, y) = 24 x - 16

Check the sign of at each critical point

Check critical point

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

Saddle

Check critical point

(2, 2) :

Maximum

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

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