Local maxima/minima and removable discontinuities

I think there is a minimum. It's just not at 0. Just because one point is removed from the function doesn't mean that the next best point(s) aren't minima. If you search on the interval (0,∞, you'll find that the minimum is very close to 0, but if you search on the interval [0,∞, you'll hit the problematic hole.

Never mind. There's no minimum. See Russt's post.