(adsbygoogle = window.adsbygoogle || []).push({}); How do I find the Critical points of a two-variable function using MATlab?

I have a problem, I cannot seem to find the critical points of a two-variable function for the life of me!

The funtion [tex]f(x,y) = 10x^2y - 5x^2 - 4y^2 - x^4 -2y^4[/tex] is supposed to have six potential critical points. I have the following:

[tex]f_x = 20yx - 10x - 4x^3[/tex]

[tex]f_y = 10x^2 - 8y - 8y^3[/tex]

For what it's worth:

[tex]\nabla f_x = (20y - 10 - 12x^2) i + (20x) j[/tex]

[tex]\nabla f_y = (20x) i + (-8-24y^2) j[/tex]

[tex]\nabla f_x = \lambda\nabla f_y[/tex]

[tex]\lambda = \frac{20y - 10 - 12x^2}{20x} = \frac{20x}{-8-24y^2}[/tex]

I know that the potential critical points are at [tex]f_x = f_y = 0[/tex], but how do I find these using MATlab, or even on paper. How would I solve for both equations?

I just can't crack this problem!

P.S. - I have MATlab version 6.5

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# How do I find the Critical points of a multi-variable function using MATlab?

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