MA 16600 Challenge problem 7Due March 7,2025 by midnight.Note: the challenge problems are being graded on process as much as results. Therefore, please show your work and explain your reasoning as much as possible. Partial credit will be given. Enact answers are preferred, but approzimate answers are acceptalle - particularly if finding an eract answer is infeasible.Let f be a concave down function (so f''(x)<0) on an interval a,b.(a) Show that Tnabf(x)dx(N.B. This should be independent of the value of n.)Find an example of a function y=g(x), an interval a,b, and a positive integer n such that Mn and Tn both err in the same direction as estimates of abg(x)dx- that is, either both are underestimates or both are overestimates. Explain your reasoning: what process did you follow to find this function MA 16600 Challenge problem 7Due March 7,2025 by midnight.Note: the challenge problems are being graded on process as much as results. Therefore, please show your work and explain your reasoning as much as possible. Partial credit will be given. Enact answers are preferred, but approzimate answers are acceptalle - particularly if finding an eract answer is infeasible.Let f be a concave down function (so f''(x)<0) on an interval a,b.(a) Show that Tnabf(x)dx(N.B. This should be independent of the value of n.)Find an example of a function y=g(x), an interval a,b, and a positive integer n such that Mn and Tn both err in the same direction as estimates of abg(x)dx- that is, either both are underestimates or both are overestimates. Explain your reasoning: what process did you follow to find this function