{"text_format":"3","workbook":"xlsx","n_sheets":2,"sheets":["Square","Sheet2"],"not_rendered":{"charts":3,"images":2,"macros":1,"defined_names":17,"comments":1},"read":"whole","date_system":"1900"}

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[null,"Volume of an Open Box Problem"]
[]
[null,"  This DIGMath module lets you investigate "]
[null,"           the calculus problem of finding"]
[null,"     the dimensions of the largest open box"]
[null,null,"    with a square base"]
[null,"  that can be made from a given amount of "]
[null,"            material for the sides and base."]
[]
[]
["What is the area A of the cardboard used?"]
[null,"          (20 - 250 square inches)",null,null,"    Area A =",{"$f":"D13","v":78},"sq in"]
[{"$nulls":3},78,{"$f":"#REF!+D13*(#REF!-#REF!)/100","v":{"$error":"#REF!"}}]
[]
[]
["  The formula for the volume function  V =",{"$nulls":3},"(Ax - x3 )/4"]
{"$rows_empty":11}
[{"$nulls":12},"Select the length x of the base: x =",null,null,{"$f":"xMin+O30*dx","v":4.55},"inches"]
[]
[{"$nulls":14},31,{"$f":"Sheet2!H7+O30*(Sheet2!H8-Sheet2!H7)/100","v":4.55}]
[]
[{"$nulls":12},"               The volume of this box is",null,null,{"$f":"(A*x0 - x0^3 )/4","v":{"v":65.17590625,"d":"65.2"}},"cubic inches"]
[]
[{"$nulls":12}," The value of the derivative is V' = ",null,null,{"$f":"(A - 3*x0^2 )/4","v":3.973125000000003}]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["      Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

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[null,"x","f(x)","f'(x)"]
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