document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=67627>Question 67627</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please Help!!! I cant figure this out.\r<BR>\n" );
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document.write( "1) 	An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.<BR>\n" );
document.write( "a) 	Find the function V that represents the volume of the box in terms of x.<BR>\n" );
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document.write( "b) 	Graph this function and show the graph over the valid range of the variable x..<BR>\n" );
document.write( "Show Graph here.<BR>\n" );
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document.write( "c) 	Using the graph, what is the value of x that will produce the maximum volume?<BR>\n" );
document.write( "Answer.  \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #48143 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=48143\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.<BR>\n" );
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document.write( "a) Find the function V that represents the volume of the box in terms of x.<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "The dimensions of the box will be (4-2x) by (6-2x) by x<BR>\n" );
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document.write( "FOIL (4-2x)(6-2x) and you have: 24 - 20x + 4x^2, mult that x,<BR>\n" );
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document.write( "V(x) = 4x^3 - 20x^2 + 24x<BR>\n" );
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document.write( "b) Graph this function and show the graph over the valid range of the variable x..<BR>\n" );
document.write( "Show Graph here.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-2%2C+3%2C+-4%2C+10%2C+4x%5E3+-+20x%5E2+%2B+24x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-2%2C+3%2C+-4%2C+10%2C+4x%5E3+-+20x%5E2+%2B+24x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c) Using the graph, what is the value of x that will produce the maximum volume?<BR>\n" );
document.write( "Answer.<BR>\n" );
document.write( "It looks like that about x =.75 ft will produce max volume (8.4 cu ft)<BR>\n" );
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document.write( "You can find out exactly for x = .75: (4-1.5) * (6-1.5) * .75 = 8.4375<BR>\n" );
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document.write( "My Ti83 gave the max at x = .78475 produces a max vol of 8.45 cu ft<BR>\n" );
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document.write( "Did this help you?\r<BR>\n" );
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