document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1032139>Question 1032139</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Consider the function y = f(x) ={( x + 1/ x - 2)}^3<BR>\n" );
document.write( "(a) Find the derivative of f.<BR>\n" );
document.write( "(b) Find the equations of the tangent and the normal to the curve y = f(x) at the point (1,-8).<BR>\n" );
document.write( "(c) Find all the values of x so that f'(x) < 0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #646812 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=646812\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+f%28x%29+=+%28+%28x+%2B+1%29%2F%28+x+-+2%29%29%5E3+ ALIGN=MIDDLE  ALT=\"y+=+f%28x%29+=+%28+%28x+%2B+1%29%2F%28+x+-+2%29%29%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> y' = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28%28x+%2B+1%29%2F%28+x+-+2%29%29%5E2%2A%28%28%28x-2%29%2A1+-+%28x%2B1%29%2A1%29%2F%28x-2%29%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9%28x%2B1%29%5E2%29%2F%28x-2%29%5E4 ALIGN=MIDDLE  ALT=\"%28-9%28x%2B1%29%5E2%29%2F%28x-2%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(b)  f'(1) = -36 after substitution into the previous equation for y'.\r<BR>\n" );
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document.write( "==> the equation of the tangent at (1, -8) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bt%5D+%2B+8+=+-36%28x-1%29 ALIGN=MIDDLE  ALT=\"y%5Bt%5D+%2B+8+=+-36%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bt%5D+=+-36x+%2B+28 ALIGN=MIDDLE  ALT=\"y%5Bt%5D+=+-36x+%2B+28\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "==> the equation of the normal at (1, -8) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bn%5D+%2B+8+=+%281%2F36%29%28x-1%29 ALIGN=MIDDLE  ALT=\"y%5Bn%5D+%2B+8+=+%281%2F36%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bn%5D+=+%281%2F36%29x+-+289%2F36 ALIGN=MIDDLE  ALT=\"y%5Bn%5D+=+%281%2F36%29x+-+289%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" > after simplification.\r<BR>\n" );
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document.write( "(c)  f'(x) < 0 for all real values EXCEPT at x = 2, where there is an essential (infinite) discontinuity.  (This is because f'(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9%28x%2B1%29%5E2%29%2F%28x-2%29%5E4+%3C+0 ALIGN=MIDDLE  ALT=\"%28-9%28x%2B1%29%5E2%29%2F%28x-2%29%5E4+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > except at x=2 where it is undefined.)<BR>\n" );
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