document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=988976>Question 988976</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In consider the function 1/x \r<BR>\n" );
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document.write( "Find the slope of the line L tangent to the graph of (3,f(3)) \r<BR>\n" );
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document.write( "I know to find the slope of the tangent I use: lim h->0 f(x+h)-f(x)/h \r<BR>\n" );
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document.write( "why does this switch from that to (1/(x+h))-(1/x)/(h)? <BR>\n" );
document.write( "I thought since we have x and y values (3,f(3)) I can just somehow plug those values in. Why does x+h become 1/(x+h) \r<BR>\n" );
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document.write( "Do we first have to alter the limit definition of a derivative (tangent slope) first given the graph shape? then do some rearranging and factoring? Because I know it gets to be lim h->0 1/x^2 which makes the slope m = -1/9 <BR>\n" );
document.write( "what I also don't get is why do y become y=1/3 when the original points were (3,f(3)) \r<BR>\n" );
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document.write( "Confused so much about all this. \r<BR>\n" );
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document.write( "Please help <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 #609513 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=609513\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We are working with the limit definition of the first derivative, that is<BR>\n" );
document.write( "Limit as h --&#12299;0 of ( f(x+h) - f(x) ) / h<BR>\n" );
document.write( "We are given f(x) = 1 / x<BR>\n" );
document.write( "We apply the given function to the limit definition<BR>\n" );
document.write( "Limit as h --&#12299;0 of ( 1/(x+h) - 1/x ) / h =<BR>\n" );
document.write( "( x - x - h ) / (x(x+h)h ) =<BR>\n" );
document.write( "-h / (x^2+xh)h =<BR>\n" );
document.write( "-1 / x^2<BR>\n" );
document.write( "Note that the xh term becomes 0 as h --&#12299;0<BR>\n" );
document.write( "f(3) = 1 / 3<BR>\n" );
document.write( "m = f'(3) = -1 / 3^2 = -1 / 9\r<BR>\n" );
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