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Jun
24
comment If a function is defined on the interval $(a, b)$, is the derivative necessarily defined at $a$ and $b$?
@TravisJ no need. It's just one of those commonly misused words, and one of those rare cases when it was actually used properly :) so it is a bit ironic, but it doesn't matter since whether it was assumed, subsumed or presumed, the result would be the same :)
Jun
24
comment If a function is defined on the interval $(a, b)$, is the derivative necessarily defined at $a$ and $b$?
@TravisJ Normally, I try to avoid fighting over edits that change nothing in the question, but just out of curiosity, why did you change "subsume" to "assume"? I mean, the thing that I'm given to prove doesn't assume that, it subsumes (as in, if proved to be true, then this statement would be a particular case of some larger claim).
Jun
24
accepted If a function is defined on the interval $(a, b)$, is the derivative necessarily defined at $a$ and $b$?
Jun
24
comment If a function is defined on the interval $(a, b)$, is the derivative necessarily defined at $a$ and $b$?
Thanks, although I'm going to accept Noah Schweber's answer (simply because he was first). All answers in my eye are good. I just have to pick one to make SO rules happy.
Jun
24
comment If a function is defined on the interval $(a, b)$, is the derivative necessarily defined at $a$ and $b$?
Thanks! I'm going to accept Noah Schweber's answer just because it was the first one. Now I see that all answers are very nice, so there would be no other reason to prefer one. I'm just doing it to comply with SO rules. :)
Jun
24
comment If a function is defined on the interval $(a, b)$, is the derivative necessarily defined at $a$ and $b$?
@GitGud the assignment doesn't say that the function isn't defined anywhere outside $(a, b)$, so it could be defined, I'm just not told that it is.
Jun
24
asked If a function is defined on the interval $(a, b)$, is the derivative necessarily defined at $a$ and $b$?
Jun
24
accepted When are monic polynomials of fourth degree divisible?
Jun
24
comment When are monic polynomials of fourth degree divisible?
OK, that and en.wikipedia.org/wiki/Intermediate_value_theorem. I think I've got it now. Thanks, much appreciated!
Jun
24
comment When are monic polynomials of fourth degree divisible?
Oh, so this would be basically the proof of en.wikipedia.org/wiki/Factor_theorem, wouldn't it?
Jun
24
comment When are monic polynomials of fourth degree divisible?
Why should there be a leading term of odd degree? What if its coefficient is zero?
Jun
24
comment When are monic polynomials of fourth degree divisible?
@MichaelBurr ouch, I was thinking of something else... yes, that's definitely true.
Jun
24
comment When are monic polynomials of fourth degree divisible?
@ajotatxe if the graph of quadric function touches X axis, the root will be zero, but that possibility is already excluded in the given.
Jun
24
comment When are monic polynomials of fourth degree divisible?
@MichaelBurr fair point... I've re-read the text of assignment, and it doesn't say explicitly that the roots must be distinct, but if they shouldn't be distinct, then it's an absolute no-brainer, just by using the fundamental theorem of algebra...
Jun
24
asked When are monic polynomials of fourth degree divisible?
Jun
5
accepted Generating functions which are prime
Jun
5
asked Generating functions which are prime
Jun
4
revised What is $D(n,k)$? (dee-en-kay) /ˈdiːˈɛnˈkeɪ/
added 8 characters in body
Jun
4
accepted What is $D(n,k)$? (dee-en-kay) /ˈdiːˈɛnˈkeɪ/
Jun
4
comment What is $D(n,k)$? (dee-en-kay) /ˈdiːˈɛnˈkeɪ/
Yes, that was a copy-paste error. I also forgot the -1. For me Google returns with all kinds of answers, many are related to math, but nothing that would link this to this particular meaning. I'm starting to suspect that D was chosen simply because it follows C in the alphabet...