Please help with the following calculus questions:

Problem 2.1. Assume that f (x) =x.e-*. (i) First, find all the critical numbers of f; (ii) next, apply the Increasing/Decreasing Test to determine the interval(s) on which f is increas ing and the interval(s) on which f is decreasing; (iii) finally, for each critical number c, apply the First Derivative Test to determine whether f (c) is a local maximum or local minimum or neither. Problem 2.2. Assume that f (x) = x . e *(same as in Problem 2.1). (i) Apply the Concavity Test to determine the interval(s) on which the graph of f is concave upward and the inter- val(s) on which the graph of f is concave downward, and find all the inflection points (if any) on the graph of f; (ii) for each critical number c (found in ), apply the Second Derivative Test to determine whether f (c) is a local maximum or local minimum or neither (check against