# sketching contours

• Aug 14th 2008, 02:02 AM
sketching contours
I have the function f(x,y)= 2x^3 + 3xy + 2y^3, I have found the 2 critical points for x in R and y in R.
I believe they are (0,0) and (-1/8, 1/2)?!
I then found that they are both saddle points which is when I doubted whether these critical points are correct.
I then have to sketch the contours which I have attempted but am unsure if I have constructed the sketch correctly.
• Aug 14th 2008, 02:09 AM
mr fantastic
Quote:

I have the function f(x,y)= 2x^3 + 3xy + 2y^3, I have found the 2 critical points for x in R and y in R.
I believe they are (0,0) and (-1/8, 1/2)?!
I then found that they are both saddle points which is when I doubted whether these critical points are correct.
I then have to sketch the contours which I have attempted but am unsure if I have constructed the sketch correctly.

The equations to solve are:

$6 x^2 + 3y = 0 \Rightarrow 2 x^2 + y = 0$ .... (1)

$3x + 6 y^2 = 0 \Rightarrow x = -2 y^2$ .... (2)

Substitute (2) into (1):

$8 y^4 + y = 0 \Rightarrow y (8 y^3 + 1) = 0$

$\Rightarrow y = 0, ~ - \frac{1}{2}$ .....
• Aug 14th 2008, 02:48 AM