Sam Snyder wrote:
Also, the absolute value won't ever introduce new critical points if you're looking at zeros of the derivative, the only complex number of norm 0 is 0.
But the absolute value can introduce new critical points at zeros of a real function.
Yes, but if you want to be situation specific, zeros of the function represent the minimum, so "new critical values" would all be moot anyways, just check for zeros of the function. I mean, it's okay to be thorough with what you're doing, but if you're going that far you need to go all the way, otherwise it just sounds like you're looking for a reason to add another post to your total post-count. The most qualitative thing you could have said there was not the lack of zeros making new critical points, but rather if it were zero we would already be done.