document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=988918>Question 988918</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the function f(x) = 1/x \r<BR>\n" );
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document.write( "I cannot use derivatives, my teacher requires using limits or other methods to solve. <BR>\n" );
document.write( "(a). Find the slope of the L tangent to the graph of (3,f(3)) <BR>\n" );
document.write( "(b). Find an equation of the line L <BR>\n" );
document.write( "(c). Find the x-intercept and y-intercept of L <BR>\n" );
document.write( "Please explain how these are figured out. Very confused. \r<BR>\n" );
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document.write( "Also, what exactly is 3,f(3) are these just arb pts?<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #609370 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=609370\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The point (3,f(3)) is the same as (3,1/3) since f(3) = 1/3\r<BR>\n" );
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document.write( "Plug x = 3 into f(x) = 1/x to get f(3) = 1/3\r<BR>\n" );
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document.write( "Part a)\r<BR>\n" );
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document.write( "Let's simplify the difference quotient\r<BR>\n" );
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document.write( "Now apply the limit.\r<BR>\n" );
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document.write( "As h approaches 0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F%28x%28x%2Bh%29%29 ALIGN=MIDDLE  ALT=\"-1%2F%28x%28x%2Bh%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > will approach <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F%28x%28x%2B0%29%29+=+-1%2F%28x%2Ax%29+=+-1%2F%28x%5E2%29 ALIGN=MIDDLE  ALT=\"-1%2F%28x%28x%2B0%29%29+=+-1%2F%28x%2Ax%29+=+-1%2F%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the derivative function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F%28x%5E2%29 ALIGN=MIDDLE  ALT=\"-1%2F%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Plug x = 3 into the derivative function to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F%28x%5E2%29=-1%2F%283%5E2%29=-1%2F9 ALIGN=MIDDLE  ALT=\"-1%2F%28x%5E2%29=-1%2F%283%5E2%29=-1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, the slope of line L is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F9 ALIGN=MIDDLE  ALT=\"m=-1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Part b)\r<BR>\n" );
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document.write( "The slope of line L is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F9 ALIGN=MIDDLE  ALT=\"-1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > (found earlier). The tangent line L goes through (3,1/3) so x = 3 and y = 1/3.\r<BR>\n" );
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document.write( "Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-1%2F9 ALIGN=MIDDLE  ALT=\"m+=+-1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2F3 ALIGN=MIDDLE  ALT=\"y=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Then solve for b.\r<BR>\n" );
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document.write( "The equation of the tangent line L is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F9%29x%2B2%2F3 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F9%29x%2B2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Part c)\r<BR>\n" );
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document.write( "The y-intercept is 2/3 or the point (0,2/3). This was found in part b) above.\r<BR>\n" );
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document.write( "The x-intercept is found by plugging in y = 0 and solving for x\r<BR>\n" );
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document.write( "The x-intercept is 6, which is the same as the point (6,0)\r<BR>\n" );
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document.write( "Graph\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+1%2Fx ALIGN=MIDDLE  ALT=\"f%28x%29+=+1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in green\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F9%29x%2B2%2F3 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F9%29x%2B2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in blue (tangent line at (3,1/3))\r<BR>\n" );
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document.write( "If you need more help, or if you have any questions about the problem, feel free to email me at <BR>\n" );
document.write( "<font color=\"blue\"><code>jim_thompson5910@hotmail.com</code></font> </SPAN>\n" );
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