document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=597839>Question 597839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You want to form a rectangular pen of area, a=70 ft^2. One side of the pen is to be formed by an existing building and the other three sides by a fence. If w is the width of the sides of the rectangle perpendicular to the building, then the length of the side parallel to the building is L=70/w. The total amount of fence required is the function F=2w + 70/w, in feet. \r<BR>\n" );
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document.write( "Determine the dimensions of the rectangle that requires a minimum amount of fence. Round to decimal places.<BR>\n" );
document.write( "width =         feet<BR>\n" );
document.write( "length =        feet\r<BR>\n" );
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document.write( "I have been having difficulty with area problems. Any help would be greatly appreciated. Thanks!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378371 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=378371\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "I hope you are taking Calculus, because that is the only way I know how to solve this one.\r<BR>\n" );
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document.write( "Minimize\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ F(w)\ =\ 2w\ +\ \frac{70}{w}\">\r<BR>\n" );
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document.write( "Take the first derivative:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dF}{dw}\ =\ 2\ -\ \frac{70}{w^2}\">\r<BR>\n" );
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document.write( "Set the first derivative equal to zero and solve for the value of the independent variable at a local extremum.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\ =\ \frac{70}{w^2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2w^2\ =\ 70\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ w\ =\ \pm\sqrt{35}\">\r<BR>\n" );
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document.write( "Discard the negative root; measurements of distance less than zero are absurd in this context.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ w\ =\ \sqrt{35}\">\r<BR>\n" );
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document.write( "Take the second derivative:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{d^2F}{dw^2}\ =\ \frac{140}{w^3}\">\r<BR>\n" );
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document.write( "Which is positive for all positive values of the independent variable.  Therefore the local extreme is a minimum.\r<BR>\n" );
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document.write( "Hence the minimum amount of fence is required when the width measures <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{35}\">.  You should be able to determine the length yourself using <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE l\ =\ \frac{70}{w}\">.  Using the calculator and rounding is also up to you.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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