A cylindrical can without top is made to contain 2m3 of liquid. We want to find the dimension that will minimize the cost of the metal to make the can. (a) Express the surface area S of the can as a function of the radius r. (b) Compute lim S(r) and lim S(r). r→0+ r→+∞ (c) Find the critical point(s), make a table, and sketch S(r)
A cylindrical can without top is made to contain 2m3 of liquid. We want to find the dimension that will minimize the cost of the metal to make the can. (a) Express the surface area S of the can as a function of the radius r. (b) Compute lim S(r) and lim S(r). r→0+ r→+∞ (c) Find the critical point(s), make a table, and sketch S(r)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A cylindrical can without top is made to contain 2m3 of liquid. We want
to find the dimension that will minimize the cost of the metal to make the can.
(a) Express the surface area S of the can as a function of the radius r.
(b) Compute lim S(r) and lim S(r).
r→0+ r→+∞
(c) Find the critical point(s), make a table, and sketch S(r)
(d) What should be r and h to minimize the surface area of the can?
(e) What is the minimal surface area possible?
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