to find the absolute max/min, you need to check for local extrema in the interval. Then check f(x) at the ends of the interval to see whether they qualify as being more max/min.
f'(x) = 2/∛(x-2)
clearly that is never zero, so there are no internal local extrema.
So, now just check f(1) and f(10). They will be the absolute min and max.
Find the absolute maximum and minimum values of the function f(x)=3(x-2)^(2/3)+5 on the interval [1,10]?
I'm not sure how to do this. Please help.
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