How do you find the relative extrema for #f(x) =2x 3x^(2/3) +2# on the interval [1,3]?
1 Answer
May 25, 2015
Find and test the critical numbers for
Critical numbers for

In the domain of
#f# , and 
at which
#f'(x) = 0# or#f'(x)# does not exist.
(This is a wonderful example of why you cannot ignore the second kind of critical numbers.)
For this function, we have:
#x=1# #color(white)"ssssssssssssss"# # x =0#
Using the first derivative we find that
increasing on
decreasing on #(0,1) so