MA 16600 Challenge problem 9Due March 28,2025 by midnightNote: the challenge problems are being graded on process as much as reswits. Therefore, please show your work and explain your reasoning as mach as possible. Partial credit vill be given. Bract answers are preferred, but approrimate ansuers are acceptabte - particutarly if finding an eract answer is infeasible.Let f be a contimuous function, and define a sequence by a1=a,an1=f(an). This is called an iterated sequence of f, since we perform the same operation over and over to gencrate the sequence elements.If limnan=L show that f(L)=L.(We call a value x where f(x)=x a fixed point of f, so another way to say this is: the limit of any convergent iterated sequence of f is a fixed point of f.)Let g(x)=x3-x. Find all fixed points of g.Consider the iterated sequences of g : determine which initial values a lead to convergent sequences and which divergent. For the convergent values of a determine their limits.(Hint: think of the fixed points of g like equilibria in a differential equation: some are stable and some unstable. What we're really interested in is what's happening on the intervals between / around the fixed points.))