stationary points

[thegull]

Hello, its been over 30 years since I went to college and I'm ashamed to say im feeling rather foolish with all these youngster in the class. I am having rather a lot of problems understanding stationary points and saddles, Can anyone point me in the right direction??? I have attempted the following but am unsure of my workings.

Thank you very much


f (x,y) 3x² + 6xy + 2y³ + 12x -24y

dz/dx = x + y + 2 = 0 1.

dz/dy = x + y² - 4 = 0 2.


using 1.

y = -x -2

sub into 2. x + y² - 4 = 0

x + (-x -2) (-x -2) - 4 = 0

x + x² + 4x + 4 -4 = 0

x² + 5x = 0

x² = -5x

x = -5

Sub into 2. x + y² - 4 = 0

-5 + y + 2 = 0

y = 5-2

y = 3


so are these my points? if so how do i proceed to get the other two ???? I'm rather confused !!!!

so my first points are -5,3 ????

 

[Deleted member 4993]

Hello, its been over 30 years since I went to college and I'm ashamed to say im feeling rather foolish with all these youngster in the class. I am having rather a lot of problems understanding stationary points and saddles, Can anyone point me in the right direction??? I have attempted the following but am unsure of my workings.

Thank you very much


f (x,y) 3x² + 6xy + 2y³ + 12x -24y

dz/dx = x + y + 2 = 0........................ 1.

dz/dy = x + y² - 4 = 0........................ 2.


using 1.

y = -x -2

sub into 2. x + y² - 4 = 0

x + (-x -2) (-x -2) - 4 = 0

x + x² + 4x + 4 -4 = 0

x² + 5x = 0 ? x(x+5) = 0 ? x = 0 or x= - 5

x² = -5x

x = -5

Sub into 2. x + y² - 4 = 0 ? y[sup:3jmsqcac]2[/sup:3jmsqcac] = 9 ? y = ±3

Now you have x = 0 ? y = ±2

So you have (-5, -3), (-5,3), (0,-2) & (0,2) as your solutions.

Go back to your original equation and check whether all the points are within the domain of the function.

-5 + y + 2 = 0

y = 5-2

y = 3


so are these my points? if so how do i proceed to get the other two ???? I'm rather confused !!!!

so my first points are -5,3 ????

 

[thegull]

thanks you very much.

so there's 4 stationary points not just 2?

so to find out the saddle point, minimum point you put all 4 points into the grid under X and Y and work it through?