document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040468>Question 1040468</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the following, rounded to two decimal places. (Enter your answers using interval notation.)\r<BR>\n" );
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document.write( "Y=X4^(x)\r<BR>\n" );
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document.write( "(a) the intervals on which the function is increasing or decreasing?\r<BR>\n" );
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document.write( "(b) the range of the function? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655507 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=655507\">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=y=x%2A4%5Ex ALIGN=MIDDLE  ALT=\"y=x%2A4%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the derivative,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=4%5Ex%28x%2Aln%284%29%29%2B4%5Ex ALIGN=MIDDLE  ALT=\"dy%2Fdx=4%5Ex%28x%2Aln%284%29%29%2B4%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=4%5Ex%28x%2Aln%284%29%2B1%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=4%5Ex%28x%2Aln%284%29%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the sign of the derivative is controlled by,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Aln%284%29%2B1 ALIGN=MIDDLE  ALT=\"x%2Aln%284%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So find when,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Aln%284%29%2B1=0 ALIGN=MIDDLE  ALT=\"x%2Aln%284%29%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Aln%284%29=-1 ALIGN=MIDDLE  ALT=\"x%2Aln%284%29=-1\"   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%2Fln%284%29 ALIGN=MIDDLE  ALT=\"x=-1%2Fln%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The function is decreasing when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-1%2Fln%284%29 ALIGN=MIDDLE  ALT=\"x%3C-1%2Fln%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The function is increasing when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E-1%2Fln%284%29 ALIGN=MIDDLE  ALT=\"x%3E-1%2Fln%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and it has a minimum when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2Fln%284%29 ALIGN=MIDDLE  ALT=\"x=-1%2Fln%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2Fln%284%29 ALIGN=MIDDLE  ALT=\"x=-1%2Fln%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2F%28e%2Aln%284%29%29 ALIGN=MIDDLE  ALT=\"y=-1%2F%28e%2Aln%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the range is <BR>\n" );
document.write( "[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Fln%284%29 ALIGN=MIDDLE  ALT=\"-1%2Fln%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=dfc1.JPG\">. </SPAN>\n" );
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