document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=996073>Question 996073</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f (x) = e^x - e^4x <BR>\n" );
document.write( "Find all extreme values (if any) of f on the interval [0, 1]. Determine at which numbers in the interval these values occur. \r<BR>\n" );
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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 #614645 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=614645\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Step 1) Apply the derivative (use chain rule)<BR>\n" );
document.write( "f(x) = e^x - e^(4x)<BR>\n" );
document.write( "f ' (x) = e^x - 4*e^(4x)\r<BR>\n" );
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document.write( "Step 2) Solve f ' (x) = 0 for x to find the critical values<BR>\n" );
document.write( "f ' (x) = e^x - 4*e^(4x)<BR>\n" );
document.write( "0 = e^x - 4*e^(4x)<BR>\n" );
document.write( "e^x = 4*e^(4x)<BR>\n" );
document.write( "e^x/[e^(4x)] = 4<BR>\n" );
document.write( "e^(x-4x) = 4<BR>\n" );
document.write( "e^(-3x) = 4<BR>\n" );
document.write( "-3x = ln(4)<BR>\n" );
document.write( "x = (-1/3)*ln(4)<BR>\n" );
document.write( "x = -0.462098 ... this is approximate\r<BR>\n" );
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document.write( "Since the x value of -0.462098 is NOT in the interval [0,1], this means that there are NO extrema on f(x) in the interval [0,1] </SPAN>\n" );
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