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. This first example is one you may have seen in precalc. square sheet of cardboard is 3 meters long on each side. You are oing to cut out squares from each corner so that you can fold up the des to make an open box. 3 . Show that the volume of the resulting box is: 4x²-12₂² +9x² - Find the derivative of the volume with respect to x, set that erivative equal to zero and solve for x. What is the domain of interest? And what volume do we get if we use the endpoints? I I L 3 I

. This first example is one you may have seen in precalc. square sheet of cardboard is 3 meters long on each side. You are oing to cut out squares from each corner so that you can fold up the des to make an open box. 3 . Show that the volume of the resulting box is: 4x²-12₂² +9x² - Find the derivative of the volume with respect to x, set that erivative equal to zero and solve for x. What is the domain of interest? And what volume do we get if we use the endpoints? I I L 3 I

Calculus: Early Transcendentals
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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1. Optimization Examples 1. This first example is one you may have seen in precalc. A square sheet of cardboard is 3 meters long on each side. You are going to cut out squares from each corner so that you can fold up the sides to make an open box. 3 A. Show that the volume of the resulting box is: 4x²-12₂² +9x² 3_ LLLL 3 B. Find the derivative of the volume with respect to x, set that derivative equal to zero and solve for x. C. What is the domain of interest? And what volume do we get if we use the endpoints? D. Determine the maximum volume -- and convince us that we are done! I L--- 3 I I 3
Transcribed Image Text:1. Optimization Examples 1. This first example is one you may have seen in precalc. A square sheet of cardboard is 3 meters long on each side. You are going to cut out squares from each corner so that you can fold up the sides to make an open box. 3 A. Show that the volume of the resulting box is: 4x²-12₂² +9x² 3_ LLLL 3 B. Find the derivative of the volume with respect to x, set that derivative equal to zero and solve for x. C. What is the domain of interest? And what volume do we get if we use the endpoints? D. Determine the maximum volume -- and convince us that we are done! I L--- 3 I I 3
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