Let f(x)=ln(x2+2x+k) be defined for x>0, where k is a real parameter.
Answer the following:
a. (i) Find f′(x).
b. (ii) Using the expression obtained in (i), establish the condition on k that ensures f′(x)>0 for every x>0.
c. (iii) Hence determine the set of all real values of k for which f is strictly increasing on (0,∞).