document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142727>Question 1142727</A>: <I><SPAN STYLE=\"word-break: break-all;\"> **Solve using calculus optimization**\r<BR>\n" );
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document.write( "Find the point on the curve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=x%5E2+ ALIGN=MIDDLE  ALT=\"+y=x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > that is closest to the point (18, 0). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763457 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=763457\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the point on the curve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=x%5E2+ ALIGN=MIDDLE  ALT=\"+y=x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > that is closest to the point (18, 0).<BR>\n" );
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document.write( "The points on the curve are (x,x^2)<BR>\n" );
document.write( "The distance d(x) to (18,0) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x-18%29%5E2+%2B+%28x%5E2-0%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x-18%29%5E2+%2B+%28x%5E2-0%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E4+%2B+x%5E2+-+36x+%2B324%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E4+%2B+x%5E2+-+36x+%2B324%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d'(x) = (1/2)*(4x^3 + 2x - 36)/sqrt(...) = 0<BR>\n" );
document.write( "2x^3 + x - 18 = 0<BR>\n" );
document.write( "x = 2<BR>\n" );
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document.write( "The point is (2,4)<BR>\n" );
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document.write( "The distance is sqrt(16^2 + 4^2) = 4sqrt(17) units.<BR>\n" );
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