document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=61512>Question 61512</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use calculus to determine the relative extrema of f(x)=x-lnx\r<BR>\n" );
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document.write( "Find the equation of the tangent line at x=1\r<BR>\n" );
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document.write( "please help, i'm so confused! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42393 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=42393\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use calculus to determine the relative extrema of f(x)=x-lnx\r<BR>\n" );
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document.write( "Find the equation of the tangent line at x=1<BR>\n" );
document.write( "To find the relative extrema take the first derivative and find the numbers that make it 0 or undefined as long as the original function is defined there.<BR>\n" );
document.write( "f'(x)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-1%2Fx ALIGN=MIDDLE  ALT=\"1-1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=1-1%2Fx ALIGN=MIDDLE  ALT=\"0=1-1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1=-1%2Fx ALIGN=MIDDLE  ALT=\"-1=-1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=1%2Fx ALIGN=MIDDLE  ALT=\"1=1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It's undefined at 0, but so is the original function, so we can't have a relative extrema there.<BR>\n" );
document.write( "f(1)=1-ln(1)<BR>\n" );
document.write( "f(1)=1-0<BR>\n" );
document.write( "f(1)=1<BR>\n" );
document.write( "There is a relative extrema at (1,1)<BR>\n" );
document.write( "f''(x)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx%5E2 ALIGN=MIDDLE  ALT=\"1%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "f''(1)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1%5E2 ALIGN=MIDDLE  ALT=\"1%2F1%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "f''(1)=1  The second derivative is positive, so it's a local min.<BR>\n" );
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document.write( "f'(1)=1-1/1<BR>\n" );
document.write( "f'(1)=1-1<BR>\n" );
document.write( "f'(1)=0  The slope of the tangent line is 0.<BR>\n" );
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document.write( "We already found that f(1)=1<BR>\n" );
document.write( "The equation of line with the slope of 0 going through the point (1,1) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=1%29 ALIGN=MIDDLE  ALT=\"highlight%28y=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
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