document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155999>Question 1155999</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with this calculus max and min question\r<BR>\n" );
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document.write( "Find the absolute maximum and absolute minimum values of f on the given interval. (Round all answers to two decimal places.)<BR>\n" );
document.write( "f(x) = x(e^-x^2/98)<BR>\n" );
document.write( "[-4, 14] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #778740 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=778740\">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=f%28x%29+=+matrix%282%2C1%2C%22%22%2Cx%2A%28e%5E%28-x%5E2%2F98%29%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+matrix%282%2C1%2C%22%22%2Cx%2A%28e%5E%28-x%5E2%2F98%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14 ALIGN=MIDDLE  ALT=\"14\"   DISABLED_style= \"max-width:90%; height:auto;\" >]\r<BR>\n" );
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document.write( "derivate to find critical points:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29+=+-%281%2F49%29%2Amatrix%282%2C1%2C%22%22%2Ce%5E%28-x%5E2%2F98%29%29%2A%28x%5E2+-+49%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "equal to zero:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F49%29%2A+matrix%282%2C1%2C%22%22%2Ce%5E%28-x%5E2%2F98%29%29+%2A%28x%5E2+-+49%29=0 ALIGN=MIDDLE  ALT=\"-%281%2F49%29%2A+matrix%282%2C1%2C%22%22%2Ce%5E%28-x%5E2%2F98%29%29+%2A%28x%5E2+-+49%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ......since  will be equal to zero if\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C%22%22%2Ce%5E%28-x%5E2%2F98%29%29+=0 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C%22%22%2Ce%5E%28-x%5E2%2F98%29%29+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+49%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+49%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C%22%22%2Ce%5E%28-x%5E2%2F98%29+%29+=0 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C%22%22%2Ce%5E%28-x%5E2%2F98%29+%29+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> solution does not exist\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+49%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+49%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+7%29%28x%2B7%29=0 ALIGN=MIDDLE  ALT=\"%28x+-+7%29%28x%2B7%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%287%29+=+matrix%282%2C1%2C%22%22%2C7%28e%5E%28-7%5E2%2F98%29%29%29 ALIGN=MIDDLE  ALT=\"f%287%29+=+matrix%282%2C1%2C%22%22%2C7%28e%5E%28-7%5E2%2F98%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%287%29+=+matrix%282%2C1%2C%22%22%2C7%28e%5E%28-49%2F98%29%29%29 ALIGN=MIDDLE  ALT=\"f%287%29+=+matrix%282%2C1%2C%22%22%2C7%28e%5E%28-49%2F98%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%287%29+=+matrix%282%2C1%2C%22%22%2C7%28e%5E%28-1%2F2%29%29%29 ALIGN=MIDDLE  ALT=\"f%287%29+=+matrix%282%2C1%2C%22%22%2C7%28e%5E%28-1%2F2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%287%29+=+7sqrt%28e%29 ALIGN=MIDDLE  ALT=\"f%287%29+=+7sqrt%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%287%29+=+11.54 ALIGN=MIDDLE  ALT=\"f%287%29+=+11.54\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-7%29+=+matrix%282%2C1%2C%22%22%2C-7%28e%5E%28-%28-7%29%5E2%2F98%29%29%29 ALIGN=MIDDLE  ALT=\"f%28-7%29+=+matrix%282%2C1%2C%22%22%2C-7%28e%5E%28-%28-7%29%5E2%2F98%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-7%29+=+matrix%282%2C1%2C%22%22%2C-7%28e%5E%28-49%2F98%29%29%29 ALIGN=MIDDLE  ALT=\"f%28-7%29+=+matrix%282%2C1%2C%22%22%2C-7%28e%5E%28-49%2F98%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-7%29+=+matrix%282%2C1%2C%22%22%2C-7%28e%5E%28-1%2F2%29%29%29 ALIGN=MIDDLE  ALT=\"f%28-7%29+=+matrix%282%2C1%2C%22%22%2C-7%28e%5E%28-1%2F2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-7%29+=+-7sqrt%28e%29 ALIGN=MIDDLE  ALT=\"f%28-7%29+=+-7sqrt%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%287%29+=+-11.54 ALIGN=MIDDLE  ALT=\"f%287%29+=+-11.54\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "both solutions are in given interval\r<BR>\n" );
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document.write( "use second derivative test to determine at what point is maximum and minimum:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >''<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29+=%28d%2Fdx%29%28-%281%2F49%29%2A+matrix%282%2C1%2C%22%22%2C%28e%5E%28-x%5E2%2F98%29%29%2A+%28x%5E2+-+49%29%29%29+=+matrix%282%2C1%2C%22%22%2C%28e%5E%28-x%5E2%2F98%29%29%2A+x%2A+%28x%5E2+-+147%29%29%2F2401 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C%22%22%2C%28e%5E%28-7%5E2%2F98%29%29+%2A7+%28-147+%2B+7%5E2%29%29%2F2401=-0.1732944742 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >=> negative, so at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=max ALIGN=MIDDLE  ALT=\"max\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C%22%22%2C%28e%5E%28-%28-7%29%5E2%2F98%29%29+%2A-7+%28-147+%2B+%28-7%29%5E2%29%29%2F2401=0.1732944742 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >=> positive, so at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a  min\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2A%28e%5E%28-x%5E2%2F98%29%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2A%28e%5E%28-x%5E2%2F98%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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