document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1127558>Question 1127558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation of a curve is y=3+4x-x^2.<BR>\n" );
document.write( "Show that the equation of the normal to the curve at a point (3,6) is 2y=x+9.<BR>\n" );
document.write( "Given that the normal meets the coordinate axes at points A and B ,find the coordinates of midpoint of AB. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743968 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=743968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The function is y = -x^2+4x+3<br><BR>\n" );
document.write( "The derivative is -2x+4<br><BR>\n" );
document.write( "The derivative at x=3 is -2(3)+4 = -2; so the slope of the curve at x=3 is -2.<br><BR>\n" );
document.write( "The slope of the normal to the curve at x=3 is the negative reciprocal, 1/2.<br><BR>\n" );
document.write( "The equation of the line with slope 1/2 passing through (3,6) is y = (1/2)x+9/2, or 2y = x+9.<br><BR>\n" );
document.write( "The x-intercept of the normal (set y=0) is (-9,0); the y-intercept (set x=0) is (0,9/2).<br><BR>\n" );
document.write( "The midpoint of the segment with endpoints (-9,0) and (0,9/2) is (-9/2,9/4).<br><BR>\n" );
document.write( "A graph....<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-12%2C12%2C-12%2C12%2C-x%5E2%2B4x%2B3%2C%281%2F2%29x%2B9%2F2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-12%2C12%2C-12%2C12%2C-x%5E2%2B4x%2B3%2C%281%2F2%29x%2B9%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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