document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202007>Question 202007</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there, could someone please help me with the following Advanced Functions problem worth 10 marks?<BR>\n" );
document.write( "a)Determine the slope of the tangent to y=1/(1-x) at the point (2,-1) without constructing a table. Explain what you are doing.<BR>\n" );
document.write( "b)Determine the general equation of the secant from any point (A,f(A)) to the point on f(x)=4x where x=2. Describe how you would use this to find the equation of the tangent at the point (2,f(2)). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152584 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=152584\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y= 1/(1-x)<BR>\n" );
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document.write( "to  find  slope ,,,find  differential  of  above (y')<BR>\n" );
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document.write( "form  is  d/dx (C/u),,,where  c=1, u=(1-x),, du/dx = -1,, u^2 = (x^2 -2x +1)<BR>\n" );
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document.write( "d/dx(C/u) = (-1/u^2 )d/dx(u) = -1/(x^2-2x+1) * (-1) = 1/(x^2 -2x+1)=y'<BR>\n" );
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document.write( "at (2,-1) slope  is y' = 1/(x^2 -2x+1) = 1/{(2)^2 -2(2) +1} = 1<BR>\n" );
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document.write( "for  y=4x,,,,y' = 4  (always  as  y=4x  is  a  straight  line.)<BR>\n" );
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document.write( "secant  to  straight  line  is  that  straight  line,,,y=4x.<BR>\n" );
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document.write( "tan  at  (2,8) is  y=mx+b,  m=-1/4,,y=(-1/4)x +b,,,<BR>\n" );
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document.write( "subst(2,8),,,8=(-1/4)2 +b,,,b=8.5,,,,eqn  is  ,,,y=(-1/4)x +8.5<BR>\n" );
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document.write( "or  4y = -x + 34 </SPAN>\n" );
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