A taxi company charges a flat fare of Rs 60 for any trip up to and including 4 km. For every additional kilometre (or part thereof) beyond 4 km, the charge is Rs 12 per kilometre. For a trip of d kilometres (d>0), let the average cost per kilometre be C(d) rupees.
a. (i) Write C(d) as a single algebraic expression valid for all d>0 by taking into account the two charging slabs.
b. (ii) Find all critical points of C(d) for d>0, clearly indicating where C′(d) may fail to exist.
c. (iii) Determine the trip length that minimises the average cost per kilometre and calculate this minimum average cost.