document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170636>Question 1170636</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the function 𝑓(𝑥)=3𝑥⁵−5𝑥³ which is defined on [-3, 3]<BR>\n" );
document.write( "a) Draw the graph of this function.<BR>\n" );
document.write( "b) Identify the optimal point(s) of this function.<BR>\n" );
document.write( "c) Find the global max and min points of this function. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795530 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=795530\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+3x%5E5+-+5x%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29+=+3x%5E5+-+5x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > defined on [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >]\r<BR>\n" );
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document.write( "Identify the optimal point(s) of this function.\r<BR>\n" );
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document.write( "Find the global max and min points of this function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >-intercepts:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%283x%5E2+-+5%29x%5E3 ALIGN=MIDDLE  ALT=\"0+=+%283x%5E2+-+5%29x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> <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;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%283x%5E2+-+5%29 ALIGN=MIDDLE  ALT=\"0+=+%283x%5E2+-+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+=+%283x%5E2+-+5%29 ALIGN=MIDDLE  ALT=\"5+=+%283x%5E2+-+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F3+=+x%5E2 ALIGN=MIDDLE  ALT=\"5%2F3+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B-sqrt%285%2F3%29+ ALIGN=MIDDLE  ALT=\"x=%2B-sqrt%285%2F3%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=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >-intercepts are at: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%2F3+%29 ALIGN=MIDDLE  ALT=\"sqrt%285%2F3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%285%2F3+%29 ALIGN=MIDDLE  ALT=\"-sqrt%285%2F3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"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=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >-intercept:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+3%2A0%5E5+-+5%2A0%5E3=0 ALIGN=MIDDLE  ALT=\"f%28x%29+=+3%2A0%5E5+-+5%2A0%5E3=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=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >-intercept at: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "global max : \r<BR>\n" );
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document.write( "use first derivative test<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29%283x%5E5+-+5x%5E3%29+=5%2A3x%5E4-3%2A5x%5E2 ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29%283x%5E5+-+5x%5E3%29+=5%2A3x%5E4-3%2A5x%5E2\"   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=%28d%2Fdx%29%283x%5E5+-+5x%5E3%29+=15x%5E4-15x%5E2 ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29%283x%5E5+-+5x%5E3%29+=15x%5E4-15x%5E2\"   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=%28d%2Fdx%29%283x%5E5+-+5x%5E3%29+=+15x%5E2%28x%5E2+-+1%29 ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29%283x%5E5+-+5x%5E3%29+=+15x%5E2%28x%5E2+-+1%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=%28x%5E2+-+1%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+1 ALIGN=MIDDLE  ALT=\"x%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><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;\" > or <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;\" >\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+3%2A1%5E5+-+5%2A1%5E3=-2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+3%2A1%5E5+-+5%2A1%5E3=-2\"   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%28x%29+=+3%2A%28-1%29%5E5+-+5%2A%28-1%29%5E3=-3-%28-5%29=-3%2B5=2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+3%2A%28-1%29%5E5+-+5%2A%28-1%29%5E3=-3-%28-5%29=-3%2B5=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "max{ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%5E5+-+5x%5E3 ALIGN=MIDDLE  ALT=\"+3x%5E5+-+5x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > } =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2 ALIGN=MIDDLE  ALT=\"+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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;\" ><BR>\n" );
document.write( "and <BR>\n" );
document.write( "min { <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E5+-+5x%5E3 ALIGN=MIDDLE  ALT=\"3x%5E5+-+5x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > } =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2 ALIGN=MIDDLE  ALT=\"+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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;\" >\r<BR>\n" );
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document.write( "use given interval as critical points:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29+=+3%2A%28-3%29%5E5+-+5%2A%28-3%29%5E3=-594 ALIGN=MIDDLE  ALT=\"f%28-3%29+=+3%2A%28-3%29%5E5+-+5%2A%28-3%29%5E3=-594\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "min (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-594 ALIGN=MIDDLE  ALT=\"+-594\"   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%283%29+=+3%2A%283%29%5E5+-+5%2A%283%29%5E3=594 ALIGN=MIDDLE  ALT=\"f%283%29+=+3%2A%283%29%5E5+-+5%2A%283%29%5E3=594\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "max(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=594 ALIGN=MIDDLE  ALT=\"594\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );