document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999602>Question 999602</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please check my work for max/min problem.\r<BR>\n" );
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document.write( "Find the max/min of:<BR>\n" );
document.write( "f(x) = 2x^3 - 3x^2 + 6 of f on [-1,1]\r<BR>\n" );
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document.write( "f'(x) = 6x^2 - 6x<BR>\n" );
document.write( "f'(x) = 6x(x-1)<BR>\n" );
document.write( "therefore, x = 0 & x = 1 and including the boundary x = -1\r<BR>\n" );
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document.write( "testing...<BR>\n" );
document.write( "f\"(x) = 12x - 6<BR>\n" );
document.write( "f\"(0) = 12(0) - 6 = -6 < 0, MAX value occurs at x = 0<BR>\n" );
document.write( "f'(1) = 12(1) - 6 = +6 > 0, MIN value occurs at x = 1<BR>\n" );
document.write( "f\"(-1) = 12(-1) - 6 = -18 < 0, MAX value occuras at x = -1\r<BR>\n" );
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document.write( "This confuses me because now I have one MIN value that occurs at x = 1, but this isn't actually the value of the MIN just where it occurs right?<BR>\n" );
document.write( "And then I have two MAX's which one is the real max? because I think I am only dealing with rel max/min so I don't think two would make sense.\r<BR>\n" );
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document.write( "Plese explain<BR>\n" );
document.write( "Thank you\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #617197 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=617197\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Yes, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > are two extrema values.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the relative maximum.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the relative minimum.<BR>\n" );
document.write( "However since you're in an interval, you need to check the endpoints and there is a definite min and max. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=2%281%29%5E3-3%281%29%5E2%2B6=2-3%2B6=5 ALIGN=MIDDLE  ALT=\"f%281%29=2%281%29%5E3-3%281%29%5E2%2B6=2-3%2B6=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=2%28-1%29%5E3-3%28-1%29%5E2%2B6=-2-3%2B6=1 ALIGN=MIDDLE  ALT=\"f%28-1%29=2%28-1%29%5E3-3%28-1%29%5E2%2B6=-2-3%2B6=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So in the interval, the minimum occurs at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the maximum occurs at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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