Prove that a positive monic polynomial with even degree has a minima but not a maxima. You may use the fact that there are finitely many critical points.
Let's take the worst case where the first derivative has a single zero.
Let the polynomial be $f(x)$
We know $f'(c) = 0$ because $f'(...
Do we need rolles-theorem? This tag was created not so long ago and at the moment it contains this question.
If we are supposed to be consistent with the previous discussions about individual theorems from calculus, it should probably be removed: Tag proposal: mean-value-theorem
I will point ...
@A---B I have made a post on meta about recently created (rolles-theorem) tag. (Although it might worth discussing tags named after theorems in general.) If you have some comments about this, feel free to post on meta or in the tagging chat room. — Martin Sleziak16 secs ago
I think we should follow the convention and remove EVT, IVT, straight lines and some other tags that I have created if that is absolute necessary.
I thought we needed those tags because they reflect what is central to question and how I wanted the answer to question. For eg: If I had asked a question to solve a limit without derivative rule then I will add limits-without-lhopital tag. A question can be done in ways.
Do we need rolles-theorem? This tag was created not so long ago and at the moment it contains this question.
If we are supposed to be consistent with the previous discussions about individual theorems from calculus, it should probably be removed: Tag proposal: mean-value-theorem
I will point ...
