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section (measuring x inches to a side) and costing $100 to ship, the function V(x) = x²(400 – 4x) gives the volume of the box (in cubic inches). Find the values of x that are physically possible for such a box (called the relevant domain). Enter your answer as an interval with open parentheses: Use the first derivative to determine where the function V(x) is decreasing (within the relevant domain). Enter your answer as an interval with open parentheses: Use the second derivative to determine where the function V(x) is concave up (within the relevant domain). Enter your answer as an interval with open parentheses: Find the maximum volume we can ship for $100 (having square cross-section). cubic inches

section (measuring x inches to a side) and costing $100 to ship, the function V(x) = x²(400 – 4x) gives the volume of the box (in cubic inches). Find the values of x that are physically possible for such a box (called the relevant domain). Enter your answer as an interval with open parentheses: Use the first derivative to determine where the function V(x) is decreasing (within the relevant domain). Enter your answer as an interval with open parentheses: Use the second derivative to determine where the function V(x) is concave up (within the relevant domain). Enter your answer as an interval with open parentheses: Find the maximum volume we can ship for $100 (having square cross-section). cubic inches

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Allouette Shipping Company has a peculiar fee schedule. When determining the price to ship a rectangular box, they measure the girth plus the length and multiply the result by $0.25. For a box with a square cross- section (measuring x inches to a side) and costing $100 to ship, the function V(x) = x²(400 – 4x) gives the volume of the box (in cubic inches). Find the values of x that are physically possible for such a box (called the relevant domain). Enter your answer as an interval with open parentheses: Use the first derivative to determine where the function V(x) is decreasing (within the relevant domain). Enter your answer as an interval with open parentheses: Use the second derivative to determine where the function V(x) is concave up (within the relevant domain). Enter your answer as an interval with open parentheses: Find the maximum volume we can ship for $100 (having square cross-section). cubic inches
Transcribed Image Text:Allouette Shipping Company has a peculiar fee schedule. When determining the price to ship a rectangular box, they measure the girth plus the length and multiply the result by $0.25. For a box with a square cross- section (measuring x inches to a side) and costing $100 to ship, the function V(x) = x²(400 – 4x) gives the volume of the box (in cubic inches). Find the values of x that are physically possible for such a box (called the relevant domain). Enter your answer as an interval with open parentheses: Use the first derivative to determine where the function V(x) is decreasing (within the relevant domain). Enter your answer as an interval with open parentheses: Use the second derivative to determine where the function V(x) is concave up (within the relevant domain). Enter your answer as an interval with open parentheses: Find the maximum volume we can ship for $100 (having square cross-section). cubic inches
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