Apply a second derivative to identify a critical points as a local maximum, local minimum or saddle point for a function. You need to construct an open-top rectangular box with a square base that must hold a volume of exactly 450 cm³. The material for the base of the box costs 7 cents/cm² and the material for the sides of the box costs 7 cents/cm². Find the dimensions for a box that will minimize the cost of the materials used to construct box. Please show your answers to at least 4 decimal places. width: height: cm cm
Apply a second derivative to identify a critical points as a local maximum, local minimum or saddle point for a function. You need to construct an open-top rectangular box with a square base that must hold a volume of exactly 450 cm³. The material for the base of the box costs 7 cents/cm² and the material for the sides of the box costs 7 cents/cm². Find the dimensions for a box that will minimize the cost of the materials used to construct box. Please show your answers to at least 4 decimal places. width: height: cm cm
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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Transcribed Image Text:Apply a second derivative to identify a critical points as a local maximum, local minimum or saddle point for a
function.
You need to construct an open-top rectangular box with a square base that must hold a volume of exactly 450
cm³. The material for the base of the box costs 7 cents/cm² and the material for the sides of the box costs 7
cents/cm².
Find the dimensions for a box that will minimize the cost of the materials used to construct box. Please show
your answers to at least 4 decimal places.
width:
height:
cm
cm
Expert Solution
Step 1
The total volume is 450 cm3
We know for a rectangular box, volume =
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