document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=988900>Question 988900</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.\r<BR>\n" );
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document.write( "(a). Find the slope of the L tangent to the graph of (3,f(3))\r<BR>\n" );
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document.write( "(b). Find an equation of the line L\r<BR>\n" );
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document.write( "(c). Find the x-intercept and y-intercept of L\r<BR>\n" );
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document.write( "Please explain how these are figured out. Very confused.\r<BR>\n" );
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document.write( "Thank you<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 #609425 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=609425\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28f%28x%2Bh%29-f%28h%29%29%2Fh ALIGN=MIDDLE  ALT=\"m=%28f%28x%2Bh%29-f%28h%29%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > limit as h approaches 0<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28%281%2F%28x%2Bh%29%29-%281%2Fx%29%29%2Fh ALIGN=MIDDLE  ALT=\"m=%28%281%2F%28x%2Bh%29%29-%281%2Fx%29%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply by (x+h)/(x+h)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28%281-%28x%2Bh%29%2Fx%29%29%2F%28h%28x%2Bh%29%29 ALIGN=MIDDLE  ALT=\"m=%28%281-%28x%2Bh%29%2Fx%29%29%2F%28h%28x%2Bh%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply by x/x<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28x-x-h%29%2F%28xh%28x%2Bh%29%29 ALIGN=MIDDLE  ALT=\"m=%28x-x-h%29%2F%28xh%28x%2Bh%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-h%2F%28xh%28x%2Bh%29%29 ALIGN=MIDDLE  ALT=\"m=-h%2F%28xh%28x%2Bh%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out h.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F%28x%28x%2Bh%29%29 ALIGN=MIDDLE  ALT=\"m=-1%2F%28x%28x%2Bh%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Where x=3 and h=0<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F%283%283%2B0%29%29=-1%2F9+ ALIGN=MIDDLE  ALT=\"m=-1%2F%283%283%2B0%29%29=-1%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "ANSWER (a): m=-1/9<BR>\n" );
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document.write( "Slope is (-1/9), tangent point is (3,1/3)<BR>\n" );
document.write( "Equation in slope intercept form:<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "y=(-1/9)x+b Use tangent point to find b.<BR>\n" );
document.write( "(1/3)=(-1/9)3+b<BR>\n" );
document.write( "1/3=-1/3+b<BR>\n" );
document.write( "2/3=b Put b value in for final equation<BR>\n" );
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document.write( "ANSWER (b). Equation for tangent line is y=(-1/9)x+2/3<BR>\n" );
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document.write( "Now we know y intercept is (0,2/3), let y=0:<BR>\n" );
document.write( "0=(-1/9)x+2/3<BR>\n" );
document.write( "-2/3=(-1/9)x<BR>\n" );
document.write( "6=x<BR>\n" );
document.write( "And the x intercept is (6,0)<BR>\n" );
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document.write( "ANSWER (c): Intercepts: (6,0).(0,2/3)<BR>\n" );
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document.write( "Original function in red, tangent line in green.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C+1%2Fx%2C+%28-1%2F9%29x%2B%282%2F3%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C+1%2Fx%2C+%28-1%2F9%29x%2B%282%2F3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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