document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=44474>Question 44474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An open-box top is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and then folding up the flaps. Let x denote the length of each side of the square to be cut out.\r<BR>\n" );
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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 and show the graph over the valid range of the variable x.\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?\r<BR>\n" );
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document.write( "I have been struggling with this problem all week if it wasn't for this problem my assignment would be done. Please help if you can thanks!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #29379 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=29379\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An open-box top is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and then 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( "B) Graph this function and show the graph over the valid range of the variable x.<BR>\n" );
document.write( "C) Using the graph, what is the value of x that will produce the maximum volume? \r<BR>\n" );
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document.write( "WHEN WE CUT X LONG PIECES ON ALL 4 SIDES THE CARD<BR>\n" );
document.write( "BOARD WILL GET REDUCED BY<BR>\n" );
document.write( "X+X=2X...ALONG LENGTH AND...X+X=2X.....ALONG WIDTH<BR>\n" );
document.write( "SO OPEN BOX LENGTH = 8-2X AND WIDTH = 6-2X..AND HEIGHT<BR>\n" );
document.write( "=X ...SO VOLUME V IS GIVEN BY LEMGTH*WIDTH*HEIGHT<BR>\n" );
document.write( "V=(8-2X)(6-2X)X...DOMAIN OF V IS GIVEN BY THE FACT<BR>\n" );
document.write( "THAT LENGTH OR WIDTH CAN NOT BE NEGATIVE...CRITICAL<BR>\n" );
document.write( "VALUE BEING WIDTH WE GET ....<BR>\n" );
document.write( "8-2X>0...AND 6-2X>0...SO X <3<BR>\n" );
document.write( "RANGE.....MAXIMUM VALUE........<BR>\n" );
document.write( "V=X(8-2X)(6-2X)=X{48-16X-12X+4X^2)=4X^3-28X^2+48X...<BR>\n" );
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document.write( "OMIT THIS PORTION IF YOU DO NOT KNOW CALCULUS<BR>\n" );
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document.write( "IF YOU KNOW CALCULUS<BR>\n" );
document.write( "DV/DX=12X^2-56X+48=0..OR...3X^2-14X+12=0....<BR>\n" );
document.write( "X=(14+SQRT.(52))/6...OR......(7+SQRT.(13))/3...OR....(7-SQRT.13)/3<BR>\n" );
document.write( "X=3.54..OR...1.13.<BR>\n" );
document.write( "D2V/DX2=6X-14=- VE AT X=1.13...SO MAXIMUM VOLUME IS<BR>\n" );
document.write( "OBTAINED AT X=1.13'<BR>\n" );
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document.write( "YOU CAN SEE THAT MAXIMUM VOLUME OCCURS AT X=1.13  BY PLOTTING THE GRAPH.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-2%2C+3%2C+-10%2C+200%2C%0D%0A4%2A%28x%5E3%29-28%2A%28x%5E2%29%2B48%2Ax%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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