box with length equal to " x " times the width must have a volume of " V " cm3. Find the dimensions of the box that minimize the amount of material used. The width of the box measures = cm The length of the box measures = cm The height of the box measures =
box with length equal to " x " times the width must have a volume of " V " cm3. Find the dimensions of the box that minimize the amount of material used. The width of the box measures = cm The length of the box measures = cm The height of the box measures =
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.8: Joint And Combined Variation
Problem 6P
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A box with length equal to " x " times the width must have a volume of " V " cm3.
Find the dimensions of the box that minimize the amount of material used.
The width of the box measures =
cm
The length of the box measures =
cm
The height of the box measures =
cm
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Step 1: Introduce to the given information
VIEWStep 2: Let the variables and formulate the equation for volume
VIEWStep 3: Formulating an equation for the surface area of the box in one variable
VIEWStep 4: Differentiating the equation for surface area and finding the critical points
VIEWStep 5: Verifying the surface area is minimum at critical point using second derivative test
VIEWStep 6: Determining the dimensions of the box
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