I'm getting and having opposite signs (-ve & +ve) for , I get point = (2, -2), and
at point 2, -2 ,
at point 2,-2
so and This gives a -ve sign for delta.
I was taught that and should have the same sign but i'm not getting that here.
It seems that and don't have to be the same sign according to this site:
Where is the max, min or saddle point in f(x,y)=x<sup>2</sup>-y<sup>2</sup>?
So my solution could be correct.
the plot along the line y=-2, that the function has a minimum so the first
derivative wrt x, is zero at x=2, and the second derivative is positive.
If you look at the plot of the function you will see that a section through
the plot along the line x=2, that the function has a minimum so the first
derivative wrt y, is zero at y=-2, and the second derivative is negative.
That the first partials at a point are zero and the second have oposite signs
is guarantees that the point is a saddle point.
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But I do not know if there are 3-D graphing software for free. They usually are expensive.