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Technically speaking, setting the first derivative equal to zero only finds local extrema. To be sure that the minimum or maximum is truly the global extrema one needs to find the limit of the function at its end points.
LOL, you must have written that while I was finishing off my reply!
I can't remember...but isn't it usually the place where the derivative is equal to zero...those critical points are either maximums or minimums, and so I suppose that would be a place to start.....??
I was absent for several days on the account of me being sick...And so, I have no other resource but the MathIsFun forums in order to receive help for my homework during this late night... (I can only hope someone is online and able to help right at this moment...)