Thread: 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.

Hello,

Are a, b, c and d positive ?

we arent told anything about a,b,c and d besides what i have given u

Originally Posted by ah-bee

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.

How can min not exist? This is a fourth degree polynomial with a positive leading coefficient. Such a polynomial has to have an absolute minimum value.

-Dan

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

Originally Posted by ah-bee

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

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