document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033081>Question 1033081</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this:<BR>\n" );
document.write( "The function f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + x is a one-to-one function, and thus its inverse <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1 ALIGN=MIDDLE  ALT=\"f%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is also a function. Find the equation of the tangent line which can be drawn to the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1 ALIGN=MIDDLE  ALT=\"f%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > at the point (2,1). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647696 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=647696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E3+%2B+x ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E3+%2B+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then plugging in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the former would lead to \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28f%5E-1%28x%29%29+=+x+=+%28f%5E-1%28x%29%29%5E3+%2B+f%5E-1%28x%29 ALIGN=MIDDLE  ALT=\"f%28f%5E-1%28x%29%29+=+x+=+%28f%5E-1%28x%29%29%5E3+%2B+f%5E-1%28x%29\"   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=%28f%5E-1%28x%29%29%5E3+%2B+f%5E-1%28x%29+=+x ALIGN=MIDDLE  ALT=\"%28f%5E-1%28x%29%29%5E3+%2B+f%5E-1%28x%29+=+x\"   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=3%28f%5E-1%28x%29%29%5E2%2A%28df%5E-1%28x%29%2Fdx%29+%2B+df%5E-1%28x%29%2Fdx+=+1 ALIGN=MIDDLE  ALT=\"3%28f%5E-1%28x%29%29%5E2%2A%28df%5E-1%28x%29%2Fdx%29+%2B+df%5E-1%28x%29%2Fdx+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > after implicit differentiation\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%28f%5E-1%28x%29%29%5E2+%2B+1%29%2A%28df%5E-1%28x%29%2Fdx%29+=+1 ALIGN=MIDDLE  ALT=\"%283%28f%5E-1%28x%29%29%5E2+%2B+1%29%2A%28df%5E-1%28x%29%2Fdx%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > after factoring...\r<BR>\n" );
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document.write( "Now one particular point in the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is (2,1).\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%28f%5E-1%282%29%29%5E2+%2B+1%29%2A%28df%5E-1%282%29%2Fdx%29+=+1 ALIGN=MIDDLE  ALT=\"%283%28f%5E-1%282%29%29%5E2+%2B+1%29%2A%28df%5E-1%282%29%2Fdx%29+=+1\"   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=%283%2A%281%29%5E2+%2B1%29%2A%28df%5E-1%282%29%2Fdx%29+=+1 ALIGN=MIDDLE  ALT=\"%283%2A%281%29%5E2+%2B1%29%2A%28df%5E-1%282%29%2Fdx%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28df%5E-1%282%29%2Fdx%29+=+1 ALIGN=MIDDLE  ALT=\"4%28df%5E-1%282%29%2Fdx%29+=+1\"   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=df%5E-1%282%29%2Fdx+=+1%2F4 ALIGN=MIDDLE  ALT=\"df%5E-1%282%29%2Fdx+=+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is also the slope of the tangent line.\r<BR>\n" );
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document.write( "==> the equation of the tangent line to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > at the point (2,1) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+1+=+%281%2F4%29%28x+-+2%29 ALIGN=MIDDLE  ALT=\"y+-+1+=+%281%2F4%29%28x+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%2F4+%2B1%2F2 ALIGN=MIDDLE  ALT=\"y+=+x%2F4+%2B1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "As what would other tutors would point out later, the derivative at a point on the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to the reciprocal of the derivative of the function f(x) at the inverse point, on condition that f'(x) at the inverse point is NOT zero. </SPAN>\n" );
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