document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187848>Question 1187848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that the function f(x)= x/8 + 3/2x<BR>\n" );
document.write( "(i) Determine the turning points of the graph <BR>\n" );
document.write( "(ii) Determine  the nature  of the stationary points<BR>\n" );
document.write( "(iii) Hence  sketch the graph. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818856 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=818856\">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=+x%2F8+%2B+3%2F%282x%29+ ALIGN=MIDDLE  ALT=\"f%28x%29=+x%2F8+%2B+3%2F%282x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A turning point is a point of the graph where the graph changes from increasing to decreasing (rising to falling) or decreasing to increasing (falling to rising). \r<BR>\n" );
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document.write( "(i)\r<BR>\n" );
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document.write( "to find them, derivate\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+=+1%2F8+-+3%2F%282x%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%29+=+1%2F8+-+3%2F%282x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "equal to zero and solve for<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x ALIGN=MIDDLE  ALT=\"+x\"   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=0=+1%2F8+-+3%2F%282x%5E2%29 ALIGN=MIDDLE  ALT=\"0=+1%2F8+-+3%2F%282x%5E2%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=3%2F%282x%5E2%29=+1%2F8 ALIGN=MIDDLE  ALT=\"3%2F%282x%5E2%29=+1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........cross multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24=+2x%5E2 ALIGN=MIDDLE  ALT=\"24=+2x%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=x%5E2=12 ALIGN=MIDDLE  ALT=\"x%5E2=12\"   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=sqrt%2812%29%29 ALIGN=MIDDLE  ALT=\"x=sqrt%2812%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=x=sqrt%284%2A3%29 ALIGN=MIDDLE  ALT=\"x=sqrt%284%2A3%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;\" >=±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"x=2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2sqrt%283%29 ALIGN=MIDDLE  ALT=\"x=-2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substitute in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+x%2F8+%2B+3%2F%282x%29+ ALIGN=MIDDLE  ALT=\"f%28x%29=+x%2F8+%2B+3%2F%282x%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%28x%29=+%282sqrt%283%29%29%2F8+%2B+3%2F%282%2A2sqrt%283%29%29+ ALIGN=MIDDLE  ALT=\"f%28x%29=+%282sqrt%283%29%29%2F8+%2B+3%2F%282%2A2sqrt%283%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%28x%29=+sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29=+sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+%28-2sqrt%283%29%29%2F8+%2B+3%2F%28-2%2A2sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=+%28-2sqrt%283%29%29%2F8+%2B+3%2F%28-2%2A2sqrt%283%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%28x%29=+-sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29=+-sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "turning points are at:\r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) <BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2sqrt%283%29 ALIGN=MIDDLE  ALT=\"-2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"-sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
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document.write( "(ii) Determine  the nature  of the stationary points\r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)->Minimum<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2sqrt%283%29 ALIGN=MIDDLE  ALT=\"-2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"-sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)->Maximum\r<BR>\n" );
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document.write( "(iii)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%282sqrt%283%29%2C+sqrt%283%29%2F2%2C.12%29%2C+circle%28-2sqrt%283%29%2C+-sqrt%283%29%2F2%2C.12%29%2C+%0D%0Alocate%282sqrt%283%29%2C+sqrt%283%29%2F2%2Cp%282sqrt%283%29%2C+sqrt%283%29%2F2%29%29%2C+%0D%0Alocate%28-2sqrt%283%29%2C+-sqrt%283%29%2F2%2Cp%28-2sqrt%283%29%2C+-sqrt%283%29%2F2%29%29%2C+%0D%0Agraph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2F8+%2B+3%2F%282x%29+%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );