Consider the polynomial function f(x)=x3−3kx2+9x on the closed interval [0,3], where k∈R.
a. (i) Obtain f′(x).
b. (ii) Derive the inequalities that k must satisfy so that f′(x)≥0 for every x∈[0,3].
c. (iii) Hence find the complete range of k for which f is strictly increasing throughout [0,3].