document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=581931>Question 581931</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a derivative minimum word problem.<BR>\n" );
document.write( "It says first find the function f(x)that we want to maximize or minimize. Then differentiate to get the derivative of f(x). Then solve the derivative equal to zero to get the solution. The question I have is.\r<BR>\n" );
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document.write( "A box with rectangular sides, base and top is to have a volume of 4 cubic feet. It has a square base. If the material for the base and top costs $10 /ft^2 and the sides costs $20/ft^2 what is the least cost it can be made for?\r<BR>\n" );
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document.write( "Every time I have a question of squares, rectangles etc. I am Completely confused. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371940 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=371940\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the length of the sides of the square base, in feet, be x.<BR>\n" );
document.write( "The surface area of the base is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > square feet.<BR>\n" );
document.write( "The volume is the area of the base, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, times the height , h.<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Ax%5E2=4 ALIGN=MIDDLE  ALT=\"h%2Ax%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=4%2Fx%5E2 ALIGN=MIDDLE  ALT=\"h=4%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The surface area of the sides can be calculated as perimeter of the base, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x ALIGN=MIDDLE  ALT=\"4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > times height, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4xh ALIGN=MIDDLE  ALT=\"4xh\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and substituting the expression for h found above:<BR>\n" );
document.write( "lateral surface = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%284%2Fx%5E2%29=16%2Fx%29 ALIGN=MIDDLE  ALT=\"4x%284%2Fx%5E2%29=16%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in square feet)<BR>\n" );
document.write( "The cost for base and top, in $, is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2%2A10=20x%5E2 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2%2A10=20x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The cost for the sides is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%2Fx%29%2A20=320%2Fx ALIGN=MIDDLE  ALT=\"%2816%2Fx%29%2A20=320%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Total cost is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29=20x%5E2%2B320%2Fx ALIGN=MIDDLE  ALT=\"C%28x%29=20x%5E2%2B320%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dC%2Fdx=40x-320%2Fx%5E2=%2840x%5E3-320%29%2Fx%5E2 ALIGN=MIDDLE  ALT=\"dC%2Fdx=40x-320%2Fx%5E2=%2840x%5E3-320%29%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is zero for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%282%29=20%2A2%5E2%2B320%2F2=20%2A4%2B160=80%2B160=240 ALIGN=MIDDLE  ALT=\"C%282%29=20%2A2%5E2%2B320%2F2=20%2A4%2B160=80%2B160=240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The derivative is zero for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, negative for x<2, and positive for x>2, indicating a minimum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29 ALIGN=MIDDLE  ALT=\"C%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and that minimum cost is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C%282%29=240%29 ALIGN=MIDDLE  ALT=\"highlight%28C%282%29=240%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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