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Find the absolute max and absolute min

__Question:__

(1 pt) Let http://gauss.vaniercollege.qc.ca/web...bec85871c1.png on the interval http://gauss.vaniercollege.qc.ca/web...b98e26d921.png. Find the absolute maximum and absolute minimum of http://gauss.vaniercollege.qc.ca/web...910e13a9c1.png on this interval.

The absolute max occurs at http://gauss.vaniercollege.qc.ca/web...dfef23ff01.png ?

The absolute min occurs at http://gauss.vaniercollege.qc.ca/web...dfef23ff01.png ?

The absolute max is supposedly x = -1 and I do not know what the absolute min is. I use the two "edges" of the constraint and since when I solved for x I already got what the "edges" of the constraint then I determined the two "edges" to be the values to optimize with but I just do not understand what is going on. In addition, my calculator says (-1)^(2/3) does not exist but algebraically, I determined it to be = 1; who's right. me or the calculator? (My work is attached)

Any help would be greatly appreciated!

Thanks in advance!