The function f(x)=x2+1x+k is defined on the closed interval [1,3], where k is a real constant.
(i) Obtain f′(x).
(ii) Establish the inequality that f′(x) must satisfy on [1,3] for f to be strictly decreasing throughout the interval.
(iii) Solve the inequality obtained in (ii) to determine the range of k for which f is strictly decreasing on [1,3].