document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=289780>Question 289780</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use calculus to find the max and min of\r<BR>\n" );
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document.write( "x - 2*cos(x)\r<BR>\n" );
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document.write( "for the interval -2<= x <= 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #209871 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=209871\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find extrema, take the derivative and set it equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x-2%2Acos%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29=x-2%2Acos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%2Fdx=1-2%2A%28-sin%28x%29%29=1%2B2%2Asin%28x%29=0 ALIGN=MIDDLE  ALT=\"df%2Fdx=1-2%2A%28-sin%28x%29%29=1%2B2%2Asin%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B2%2Asin%28x%29=0 ALIGN=MIDDLE  ALT=\"1%2B2%2Asin%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asin%28x%29=-1 ALIGN=MIDDLE  ALT=\"2%2Asin%28x%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=sin%28x%29=-1%2F2 ALIGN=MIDDLE  ALT=\"sin%28x%29=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-7%2C+1%2C+-10%2C+2%2C+x-2%2Acos%28x%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-7%2C+1%2C+-10%2C+2%2C+x-2%2Acos%28x%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29=-1%2F2 ALIGN=MIDDLE  ALT=\"sin%28x%29=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-pi%2F6 ALIGN=MIDDLE  ALT=\"x=-pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5pi%2F6 ALIGN=MIDDLE  ALT=\"x=-5pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "From the graph, the maximum occurs at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5pi%2F6 ALIGN=MIDDLE  ALT=\"x=-5pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-5pi%2F6-2%2Acos%28-5pi%2F6%29 ALIGN=MIDDLE  ALT=\"f%28x%29=-5pi%2F6-2%2Acos%28-5pi%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-5pi%2F6-2%2A%28-sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=-5pi%2F6-2%2A%28-sqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-5pi%2F6%2Bsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=-5pi%2F6%2Bsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or approximately<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=fmin=-0.886 ALIGN=MIDDLE  ALT=\"fmin=-0.886\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "As you can see from the graph, solving for x only gives you the relative minimum and not the absolute minimum.<BR>\n" );
document.write( "The absolute minimum occur at the endpoints.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=fmin=f%28-2%2Api%29=-2%2Api-2%2Acos%282%2Api%29=-2%2Api-2=-8.28 ALIGN=MIDDLE  ALT=\"fmin=f%28-2%2Api%29=-2%2Api-2%2Acos%282%2Api%29=-2%2Api-2=-8.28\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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