Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
A box with a square base and open top must have a volume of 108 cm. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. Simplify your formula as much as possible. A(z) = Next, find the derivative, A'(x). A' (x) %3D Now, calculate when the derivative equals zero, that is, when A'(x) = 0. A'(x) = 0 when = We next have to make sure that this value of a gives a minimum value for the surface area. Let's use the second derivative test. Find A"(x). A"(2) = Evaluate A"() at the r-value you gave above. NOTE: Since your last answer is positive, this means that the graph of A(x) is concave up around that value, so the zero of A'(x) must indicate a local minimum for A(x).

A box with a square base and open top must have a volume of 108 cm. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. Simplify your formula as much as possible. A(z) = Next, find the derivative, A'(x). A' (x) %3D Now, calculate when the derivative equals zero, that is, when A'(x) = 0. A'(x) = 0 when = We next have to make sure that this value of a gives a minimum value for the surface area. Let's use the second derivative test. Find A"(x). A"(2) = Evaluate A"() at the r-value you gave above. NOTE: Since your last answer is positive, this means that the graph of A(x) is concave up around that value, so the zero of A'(x) must indicate a local minimum for A(x).

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
See similar textbooks
icon
Related questions
Topic Video
Question
A box with a square base and open top must have a volume of 108 cm. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. Simplify your formula as much as possible. A(z) = Next, find the derivative, A’(x). A' (x) = Now, calculate when the derivative equals zero, that is, when A'(x) = 0. A' (x) = 0 when x = We next have to make sure that this value of x gives a minimum value for the surface area. Let's use the second derivative test. Find A"(x). A"(x) = Evaluate A"(x) at the x-value you gave above. NOTE: Since your last answer is positive, this means that the graph of A(x) is concave up around that value, so the zero of A'(x) must indicate a local minimum for A(x).
Transcribed Image Text:A box with a square base and open top must have a volume of 108 cm. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. Simplify your formula as much as possible. A(z) = Next, find the derivative, A’(x). A' (x) = Now, calculate when the derivative equals zero, that is, when A'(x) = 0. A' (x) = 0 when x = We next have to make sure that this value of x gives a minimum value for the surface area. Let's use the second derivative test. Find A"(x). A"(x) = Evaluate A"(x) at the x-value you gave above. NOTE: Since your last answer is positive, this means that the graph of A(x) is concave up around that value, so the zero of A'(x) must indicate a local minimum for A(x).
Expert Solution
steps

Step by step

Solved in 6 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer