document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=37399>Question 37399</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There is no book for this problem. This is a problem asked by the professor. Please help.\r<BR>\n" );
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document.write( "1)	An open-top box is to be constructed from a 4 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" );
document.write( "Answer: \r<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.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #23045 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=23045\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well this is a bit difficult to show you without a diagram and graph, but here goes...<BR>\n" );
document.write( "Since we are cutting a length x out of both ends of both the length and the width, the dimensions of the base of the box will be (6 - 2x) by (4 - 2x).  It will have a height of x.  Therefore the function for the volume is<BR>\n" );
document.write( "V(x) = x(6 - 2x)(4 - 2x) = 4x^3 - 20x^2 + 24x<BR>\n" );
document.write( "I can't show you the graph but you know x must be less than two.<BR>\n" );
document.write( "To find the maximum volume, we take the derivative of V(x) and set it equal to zero...<BR>\n" );
document.write( "dV/dx = 12x^2 - 40x + 24 = 0   <BR>\n" );
document.write( "Now solve for x<BR>\n" );
document.write( "Use the quadratic formula to get<BR>\n" );
document.write( "x = (5 ± rad(7)) / 3<BR>\n" );
document.write( "But only one root works (as mentioned above), so the answer here is<BR>\n" );
document.write( "x = (5 - rad(7)) / 3 or about .785 feet </SPAN>\n" );
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