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Partials Diff and Stationary Points

Hello!

I've been given a question in which I need to find the local extreme points of the equation f(x,y)=x3+y3−12x2−9y2f(x,y)=x^3+y^3-12x^2-9y^2.

I've done the usual of calculating fx=3x2−24x=0,x=0,8;fy=3y2−18y=0,y=0,6f_x=3x^2-24x=0, x=0,8; f_y=3y^2-18y=0, y=0,6.

Now the problem comes with how can I tell which x coordinate corresponds with which y coordinate?
Wolfram tells me that the extreme points are (0,0) and (8,6) - but how do I know that I shouldn't be looking at (0,6) and (8,0)?

Thanks!
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Mr. Ee
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If you're not sure find the second derivative of both and try work from there.
Original post by RPowell95

Now the problem comes with how can I tell which x coordinate corresponds with which y coordinate?
Wolfram tells me that the extreme points are (0,0) and (8,6) - but how do I know that I shouldn't be looking at (0,6) and (8,0)?


All four points satisfy your first derivative equations (each x goes with each y), and you need to check all four to determine which are the local extrema.

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