document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62061>Question 62061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am not sure what this problem means so I don't know how to answer it, could someone help me please?\r<BR>\n" );
document.write( "\n" );
document.write( "The number e is the value of x in the equation y =2^x, where the slope of the line just grazing the curve at the point (0,1) equals 1. Is this true or false? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42830 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=42830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The number e is the value of x in the equation y =2^x, where the slope of the line just grazing the curve at the point (0,1) equals 1. Is this true or false?<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Rewrite as<BR>\n" );
document.write( "2=e^(ln2)<BR>\n" );
document.write( "Rewrite the equation as <BR>\n" );
document.write( "y=e^(xln2)<BR>\n" );
document.write( "Take the derivative to get:<BR>\n" );
document.write( "y'=2^x(ln2)<BR>\n" );
document.write( "Then <BR>\n" );
document.write( "y'(0)=(1)ln2=ln2<BR>\n" );
document.write( "But ln2 is not 1.<BR>\n" );
document.write( "So the answer is \"false\"<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );