document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33379>Question 33379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An open-top box is to be constructed from a 6 by 8 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.\r<BR>\n" );
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document.write( "b)Graph this function.\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" );
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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 #19835 by </B><A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><B>mukhopadhyay(490)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=19835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The dimension of the rectangular cardboard is 6 ft X 8 ft<BR>\n" );
document.write( "Let x-ft be each side of the square cut out from each of the four corners.<BR>\n" );
document.write( "The length of the open-top box would be (8-2x) ft (Note: two corners);<BR>\n" );
document.write( "The width of the open-top box would be (6-2x) ft.<BR>\n" );
document.write( "The height of the open-top box would be x ft. (if you draw a diagram, it will neatly explain the resulting dimension of the open-top box);<BR>\n" );
document.write( "The voume of a box = Length X Width X Height;<BR>\n" );
document.write( "If V(x) represents the volume function of the box:<BR>\n" );
document.write( "V(x) = x(8-2x)(6-2x);<BR>\n" );
document.write( "...............<BR>\n" );
document.write( "As far as graphing goes, this is a polynomial of degree 3. This is also bound by the restriction (domain of the function) x >= 0 and x <= 3;<BR>\n" );
document.write( ".....................<BR>\n" );
document.write( "You need a graphing calculator to  </SPAN>\n" );
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