A box with a square base and open top must have a volume of 171500 cm³. 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 , the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of z.] Simplify your formula as much as possible. Next, find the derivative, A'(x). Now, calculate when the derivative equals zero, that is, when A'(x) 0. [Hint: multiply both sides by ² .] 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"(x) = Evaluate A"(x) at the x-value you gave above.

A box with a square base and open top must have a volume of 171500 cm³. 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 , the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of z.] Simplify your formula as much as possible. Next, find the derivative, A'(x). Now, calculate when the derivative equals zero, that is, when A'(x) 0. [Hint: multiply both sides by ² .] 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"(x) = Evaluate A"(x) at the x-value you gave above.

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...

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