Question

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.

Answer 1

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.