document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=39262>Question 39262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bob has 3000 feet of fencing available to enclose a rectangular field.  \r<BR>\n" );
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document.write( "a) express the area A of rectangle as a function of x where x is the length of rectangle.\r<BR>\n" );
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document.write( "b) For what value of x is the area largest?\r<BR>\n" );
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document.write( "c) What is the maximum area? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #24708 by </B><A HREF=/tutors/aboutme.mpl?userid=Fermat><B>Fermat(136)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fermat><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=Fermat><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=24708\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  a) Length is L = 3000\r<BR>\n" );
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document.write( "If one side of the rectangle is x and the other side is y, then perimeter is<BR>\n" );
document.write( "P = 2x + 2y\r<BR>\n" );
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document.write( "But perimeter P = length of fencing = L<BR>\n" );
document.write( ".: P = L = 3000<BR>\n" );
document.write( "2x + 2y = 3000<BR>\n" );
document.write( "x + y = 1500<BR>\n" );
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document.write( "Area of rectangle, A = x*y<BR>\n" );
document.write( "A = xy <BR>\n" );
document.write( "substitute for y = 1500 - x,<BR>\n" );
document.write( "A = x(1500 - x)<BR>\n" );
document.write( "A = 1500x - x²<BR>\n" );
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document.write( " b) To get the largest area, find the turning points of A(x) = 1500x - x² to get a maximum.<BR>\n" );
document.write( "dA/dx = 1500 - 2x<BR>\n" );
document.write( "when dA/dx = 0, then A is a maximum or minimum\r<BR>\n" );
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document.write( "0 = 1500 - 2x<BR>\n" );
document.write( "2x = 1500<BR>\n" );
document.write( "x = 750<BR>\n" );
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document.write( "There is a turning point at x = 750.<BR>\n" );
document.write( "d²A/dx² = -2<BR>\n" );
document.write( "Since d²A/dx² is negative (at the turning point x = 750) then the turning point is a maximum.<BR>\n" );
document.write( "So max area is gotten when x = 750.<BR>\n" );
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document.write( "c) A = x(1500 - x)<BR>\n" );
document.write( "A = 750(1500 - 750)<BR>\n" );
document.write( "A = 750²<BR>\n" );
document.write( "A = 562,500<BR>\n" );
document.write( "============ </SPAN>\n" );
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