VBN2470
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Yep, sorry I've fixed it up for you now, what you said is right Would you mind explaining the question to me so I can see where to start and learn how to approach this type of question?For the second part I am getting
OK ThanksI did not use the hint, I did this instead:
UNSWUSYD, VBN2470? caps
OK Thanks
Another question I was sort of stuck on:
How many real zeroes does have?
Try differentiating and looking at the stationary points, they should tell you something about the way the curve moves.OK Thanks
Another question I was sort of stuck on:
How many real zeroes does have?
Never mind I got it, as and yield opposite signs. Is there another way of doing this question, using IVT or Extreme Value Theorem or some other method? For example the polynomial has only one real root, how would you be certain in finding the number of real zeroes existing?Try differentiating and looking at the stationary points, they should tell you something about the way the curve moves.
That is essentially IVT, since P(-n) and P(3) yield opposite signs for sufficiently large n (i.e. when n goes to inifinty), then there is some root in (-n, 3), similarly, P(3) and P(5) yield opposite signs, and P(5) and P(n), for sufficiently large n is yield opposite signs.Never mind I got it, as and yield opposite signs. Is there another way of doing this question, using IVT or Extreme Value Theorem or some other method?
Thanks
OK ThanksThat is essentially IVT, since P(-n) and P(3) yield opposite signs for sufficiently large n (i.e. when n goes to inifinty), then there is some root in (-n, 3), similarly, P(3) and P(5) yield opposite signs, and P(5) and P(n), for sufficiently large n is yield opposite signs.
In case anybody is curious, this is known as the 'Universal Chord Theorem'.
I'm pretty sure that this isn't the universal chord theorem. The universal chord theorem is that the numbers of the form 1/n are the ONLY real numbers such that the above theorem holds.In case anybody is curious, this is known as the 'Universal Chord Theorem'.
My fault!I'm pretty sure that this isn't the universal chord theorem. The universal chord theorem is that the numbers of the form 1/n are the ONLY real numbers such that the above theorem holds.
This is a little more subtle and difficult than the question that was asked.