1. ## multivariable critical point

Show that $z=(x+y)^2$ has infinity many critical points.
I've got the formula of the tangent plane to be $z=(a+b)(2x+y2-a-b)$ where a and b are the points they touch the surface, so they too are variables.

2. Originally Posted by superdude
Show that $z=(x+y)^2$ has infinity many critical points.
I've got the formula of the tangent plane to be $z=(a+b)(2x+y2-a-b)$ where a and b are the points they touch the surface, so they too are variables.
If you set the partial derivatives equal to zero, as a system, you should see that there are infinitely many solutions.

$\frac{dz}{dx} = 2(x+y) = 0$
$\frac{dz}{dy} = 2(x+y) = 0$

It's the set of all points 3-dimensional space such at x=-y.
I hope this helps.