Let hk:(0,∞)→R be given by hk(x)=xk+x, where k is a real parameter.
a. (i) Find hk′(x).
b. (ii) Determine the set of all k for which hk is strictly increasing on (0,∞).
c. (iii) Determine the set of all k for which hk is strictly decreasing on (0,∞).