g(x) = 100x + 64/(x+8)
why am i getting this wrong?
I don't know you are doing wrong because you haven't shown what you did or why you gave those answers!
Your first four lines appear to be correct: g'> 0 for x< -8.8, g'> 0 for -8.8< x< -8, g'< 0 for -8< x< -7.2, g'> 0 for x> -7.2.
However, then you say "Therefore g'(x) changes from - to + as x increases throught -8.8 and this implies there is a relative minimum at x= -8.8".
In fact, what you said before that is the opposite: g' is + for x< -8.8 and - for x> -8.8 so g' changes from + to - and there is a relative maximum at x= -8.8.