document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155974>Question 1155974</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Perform a first derivative test on the function f(x)= 2x^3+3x^2-120x+2; [-5,7].<BR>\n" );
document.write( "a. Locate the critical points of the given function.<BR>\n" );
document.write( "b. Use the first derivative test to locate the local maximum and minimum values.<BR>\n" );
document.write( "c. Identify the absolute minimum and maximum values of the function on the given interval(if they exist).\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 #778762 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=778762\">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=+2x%5E3%2B3x%5E2-120x%2B2 ALIGN=MIDDLE  ALT=\"f%28x%29=+2x%5E3%2B3x%5E2-120x%2B2\"   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=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >]\r<BR>\n" );
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document.write( "a. Locate the critical points of the given function.\r<BR>\n" );
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document.write( "find first derivative\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+=6x%5E2%2B6x-120 ALIGN=MIDDLE  ALT=\"+%28x%29+=6x%5E2%2B6x-120\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "set <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+=0 ALIGN=MIDDLE  ALT=\"+%28x%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=6x%5E2%2B6x-120=0 ALIGN=MIDDLE  ALT=\"6x%5E2%2B6x-120=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=6%28x%5E2%2Bx-20%29=0 ALIGN=MIDDLE  ALT=\"6%28x%5E2%2Bx-20%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "will be zero if\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx-20=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx-20=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%2B5x-20=0 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B5x-20=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%5E2-4x%29%2B%285x-20%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2-4x%29%2B%285x-20%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%28x-4%29%2B5%28x-4%29=0 ALIGN=MIDDLE  ALT=\"x%28x-4%29%2B5%28x-4%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+-+4%29+%28x+%2B+5%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+4%29+%28x+%2B+5%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> extreme points are at\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5 ALIGN=MIDDLE  ALT=\"x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use second derivative test to determine where is max and where is min\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+=12x%2B6 ALIGN=MIDDLE  ALT=\"%28x%29+=12x%2B6\"   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 ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >''<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%29+=12%28-5%29%2B6=-54 ALIGN=MIDDLE  ALT=\"%28-5%29+=12%28-5%29%2B6=-54\"   DISABLED_style= \"max-width:90%; height:auto;\" > => negative, the absolute maximum is at<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5 ALIGN=MIDDLE  ALT=\"+-5\"   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 ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >''<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29+=12%284%29%2B6=54 ALIGN=MIDDLE  ALT=\"%284%29+=12%284%29%2B6=54\"   DISABLED_style= \"max-width:90%; height:auto;\" > => positive, the absolute minimum is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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=+graph%28+600%2C+600%2C+-15%2C+15%2C+-500%2C+500%2C+2x%5E3%2B3x%5E2-120x%2B2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-15%2C+15%2C+-500%2C+500%2C+2x%5E3%2B3x%5E2-120x%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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