document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1009797>Question 1009797</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation of the tangent line to the graph of f(x)=(x^3+1)/(x^2+x+1)<BR>\n" );
document.write( "at the point whose x-coordinate is 1.\r<BR>\n" );
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document.write( "Find the equation of the tangent line to the curve   at the point (4,1).<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 #625329 by </B><A HREF=/tutors/aboutme.mpl?userid=Cromlix><B>Cromlix(4381)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Cromlix><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=Cromlix><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=625329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi there,<BR>\n" );
document.write( "f(x)=(x^3+1)/(x^2+x+1)<BR>\n" );
document.write( "f(x) = x^5 + x^4 + x^3 + x^2 + x + 1<BR>\n" );
document.write( "When x = 1 y = 6<BR>\n" );
document.write( "f'(x) = 5x^4 + 4x^3 + 3x^2 + 2x + 1<BR>\n" );
document.write( "f'(1) = 5 + 4 + 3 + 2 + 1<BR>\n" );
document.write( "f'(1) = 15 (gradient of tangent)<BR>\n" );
document.write( "Using y - b = m(x - a)<BR>\n" );
document.write( "y - 6 = 15(x - 1)<BR>\n" );
document.write( "y = 15x - 15 + 6<BR>\n" );
document.write( "y = 15x - 9<BR>\n" );
document.write( "..............<BR>\n" );
document.write( "f'(x) = 5x^4 + 4x^3 + 3x^2 + 2x + 1<BR>\n" );
document.write( "f'(4) = 1593 (Gradient of tangent)<BR>\n" );
document.write( "Using y - b = m(x - a)<BR>\n" );
document.write( "y - 1 = 1593(x - 4)<BR>\n" );
document.write( "y = 1593x - 6372 + 1<BR>\n" );
document.write( "y = 1593 - 6371<BR>\n" );
document.write( "..................<BR>\n" );
document.write( "Hope this helps :-) </SPAN>\n" );
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