What is the extreme f(x,y)=y^3+x^2-6xy+3x+6y-7 ?

The extreme f(x,y)=y^3+x^2-6xy+3x+6y-7 is Minimum(27/2 ,5),Saddle(3/2 ,1)

Popular >

extreme f(x,y)=y^3+x^2-6xy+3x+6y-7

extreme points

f (x, y) = y^{3} + x^{2} - 6 x y + 3 x + 6 y - 7

Minimum (\frac{27}{2}, 5), Saddle (\frac{3}{2}, 1)

Solution steps

Find the critical points:

(\frac{27}{2}, 5), (\frac{3}{2}, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 6 y

D (x, y) = 12 y - 36

Check the sign of at each critical point

Check critical point

(\frac{27}{2}, 5) :

Minimum

Check critical point

(\frac{3}{2}, 1) :

Saddle

Minimum (\frac{27}{2}, 5), Saddle (\frac{3}{2}, 1)

f (x, y) = x^{2} + x y + y^{2} - 3 x - 6 y

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

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

f (x) = \frac{x ^{2} - 1}{x ^{2} + 1}, - 5 \leq x \leq 5

f (x, y) = \frac{1}{2} x^{4} - 3 x y + 3 y^{4}

What is the extreme f(x,y)=y^3+x^2-6xy+3x+6y-7 ?
The extreme f(x,y)=y^3+x^2-6xy+3x+6y-7 is Minimum(27/2 ,5),Saddle(3/2 ,1)