Chapter 6.3, Problem 17E

A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.

How are the absolute maximum and minimum similar to and different from the local extrema?

3. Consider the function f (x) = sin² x + sin x on the interval (0,27). a) Find the open interval on which the function is increasing or decreasing. b) Apply the First Derivative Test to identify all local extrema.