Hello,

Are a, b, c and d positive ?

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- Apr 24th 2008, 11:29 PM #1

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## Sup, Max, Inf, Min

Where the sup, inf, max and min exist, determine their value.

B = {x is real | (x-a)(x-b)(x-c)(x-d) < 0} for some given fixed real numbers a,b,c,d such that a<b<c<d.

i already know that the inf and min do not exist, but how can i determine the max and sup, i tried differentiation to get the max.. but...... TOO MANY VARIABLES lol.

- Apr 24th 2008, 11:31 PM #2

- Apr 24th 2008, 11:31 PM #3

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- Apr 25th 2008, 04:13 AM #4

- Apr 25th 2008, 04:28 AM #5

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hmm in that case, does that mean that the supremum is 0 and the max doesnt exist and how would i find the infimum and the min then. i have also realised that it was a mistake on my part, i made a faulty assumption in my initial post. but that doesnt change the fact that im still baffled by this question.. lol

- Apr 25th 2008, 07:59 AM #6
I can't say anything about the supremum, you are right that max doesn't exist. I can't solve for the min because we don't know a, b, c, and d. You would need to solve a cubic equation and whereas that's possible to do with just variables it is annoying. For instance we don't know if there is one absolute min or two local mins.

-Dan