WRITTEN ASSIGNMENT 6: MONOTONICITY, CONCAVITY, & APPLICATIONS CALCULUS 1, SPRING 2023 MATH 1210-090 INSTRUCTOR: WILL FELDMAN Name: uID: Problem 1. Consider the function f(x) = 243 _5x1/3 (a) Find f(x). (b) Find the critical points of f(x) and state whether each one is a stationary point or a singular point.2 CALCULUS 1, SPRING 2023 MATH 1210-090 INSTRUCTOR: WILL FELDMAN (c) Use the First Derivative Test to classify each critical point found in (b) as a local minimum, local maximum, or neither. Problem 2. A manufacturer is making cylindrical cans with radius r and height h. Corporate says the volume of the cans must be 550 mL (i.e. cm*) exactly. Corporate also says the base of the can should be made out of a "smart wifi-enabled" material that tracks consumer can use patterns. This material costs 2 times as much as the material used for the sides and top of the can. What are the dimensions r and h of the can that minimize the total cost