document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=894730>Question 894730</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This time rectangle R has varying length l and width w but with a constant area of 4 square feet.<BR>\n" );
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document.write( "Express the perimeter P as a function of length l<BR>\n" );
document.write( "What type of function is P? What is the domain of P?<BR>\n" );
document.write( "b)Describe the asymptotic behavior of P. What can you say about rectangle R because of this behavior? Could you have made a similar statement about R back in Task 1?<BR>\n" );
document.write( "c)<BR>\n" );
document.write( "For what values of l and w will the perimeter of R be the least? <BR>\n" );
document.write( "Give a geometric explanation. Be sure to include a graph with relevant points labeled.\r<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 #542266 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=542266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> l is a bad choice for length.  Choose L for length.\r<BR>\n" );
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document.write( "A is area and is constant A=4.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=wL=A ALIGN=MIDDLE  ALT=\"wL=A\"   DISABLED_style= \"max-width:90%; height:auto;\" >;  perimeter p is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2w%2B2L ALIGN=MIDDLE  ALT=\"p=2w%2B2L\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=A%2FL ALIGN=MIDDLE  ALT=\"w=A%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" > allows for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2%28A%2FL%29%2B2L ALIGN=MIDDLE  ALT=\"p=2%28A%2FL%29%2B2L\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Domain for p is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%3E0 ALIGN=MIDDLE  ALT=\"L%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Knowing that A=4, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2%284%2FL%29%2B2L ALIGN=MIDDLE  ALT=\"p=2%284%2FL%29%2B2L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=8%2FL%2B2L ALIGN=MIDDLE  ALT=\"p=8%2FL%2B2L\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Further,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=8%2FL%2B2L%5E2%2FL ALIGN=MIDDLE  ALT=\"p=8%2FL%2B2L%5E2%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=%288%2B2L%5E2%29%2FL ALIGN=MIDDLE  ALT=\"p=%288%2B2L%5E2%29%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2%284%2BL%5E2%29%2FL ALIGN=MIDDLE  ALT=\"p=2%284%2BL%5E2%29%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is a rational function, and there is an asymptote for L=0.\r<BR>\n" );
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document.write( "L^2 becomes smaller faster than L, as L approaches 0, but looking at the separate terms 8/L and 2L^2/L, seeing 8/L increases while 2L^2/L will decrease without bound as L approaches 0.  The function p of L will increase without bound as L approaches 0.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-1%2C12%2C-1%2C12%2C8%2Fx%2B2x%5E2%2Fx%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1%2C12%2C-1%2C12%2C8%2Fx%2B2x%5E2%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You might try derivative and look for the local minimum, but the graph shows a minimum perimeter at about L=2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-1%2C4%2C-1%2C12%2C8%2Fx%2B2x%5E2%2Fx%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1%2C4%2C-1%2C12%2C8%2Fx%2B2x%5E2%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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