Problem 1. Consider the function x) : 11233 :1: 1. Answer the following questions and use your answers to sketch an accurate graph of f (x) No need to use a calculator! (a) Find f'(:r). (b) Find the critical points of f. (c) Find the interval(s) on Which f is increasing and the interval(s) on which f is decreasing. 2 CALCULUS I, FALL 2022 MATH 1210-090 INSTRUCTOR: WILL FELDMAN (d) Find f"(x). (e) Find the interval(s) on which f is concave up and the interval(s) on which f is concave down. (f) Find any inflection points of f. (g) Finally, use the previous information to sketch the graph of the func- tion, marking the critical points with a small circle and inflection points of f with a small cross. (Make sure to evaluate the function at least at the critical points and inflection points to place them accurately)