[8] Let f be differentiable on R with A = suplf'(:c)|; cc 6 R and A

[8] Let f be differentiable on IR with A = e IR and A < 1. For a given value of ao , f(an-l), n 2 1. define the sequence an by an = a. b. c. d. Show that Ian +1 anl Alan anII for n 2 1. Deduce that {an} is a cauchy sequence and hence convergent. Deduce that the graph of f@) must cross the line y = x. How many times can it do so?