document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=26217>Question 26217</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1)	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.<BR>\n" );
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document.write( "b)	Graph this function.<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 #19510 by </B><A HREF=/tutors/aboutme.mpl?userid=danirivera5><B>danirivera5(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=danirivera5><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=19510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4/10/06\r<BR>\n" );
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document.write( "..(IN YOUR CASE 8-2X)  AND WIDTH = 15-2X..(IN YOUR CASE 6-2X)..AND HEIGHT =X ...SO VOLUME V IS GIVEN BY LEMGTH*WIDTH*HEIGHT <BR>\n" );
document.write( "V=(25-2X)(15-2X)X...(IN YOUR CASE (8-2X)(6-2X)X...DOMAIN OF V IS GIVEN BY THE FACT THAT LENGTH OR WIDTH CAN NOT BE NEGATIVE...CRITICAL VALUE BEING WIDTH WE GET .... <BR>\n" );
document.write( "15-2X>0...OR....15>2X...OR....7.5>X....OR X<7.5...(IN YOUR CASE 8-2X>0...AND 6-2X>0...SO X <3)<BR>\n" );
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document.write( "RANGE.....MAXIMUM VALUE....IN YOUR CASE....<BR>\n" );
document.write( "V=X(8-2X)(6-2X)=X{48-16X-12X+4X^2)=4X^3-28X^2+48X...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 OBTAINED AT X=1.13'<BR>\n" );
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