document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205395>Question 1205395</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch the graph of the following functions by using the conditions of concavity f(x)=(x^2-16)^4<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 #842195 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=842195\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x%5E2+-+16%29%5E4 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x%5E2+-+16%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find second 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+=++8x+%28x%5E2+-+16%29%5E3 ALIGN=MIDDLE  ALT=\"%28x%29+=++8x+%28x%5E2+-+16%29%5E3\"   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=%28x%29+=+8+%28x%5E2+-+16%29%5E2+%287x%5E2+-+16%29+ ALIGN=MIDDLE  ALT=\"%28x%29+=+8+%28x%5E2+-+16%29%5E2+%287x%5E2+-+16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <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;\" > when\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+%28x%5E2+-+16%29%5E2+%287x%5E2+-+16%29+=0 ALIGN=MIDDLE  ALT=\"8+%28x%5E2+-+16%29%5E2+%287x%5E2+-+16%29+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "critical points of the derivatives are:\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;\" > => stationary<BR>\n" );
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;\" >=> stationary<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4%2Fsqrt%287%29 ALIGN=MIDDLE  ALT=\"x=4%2Fsqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> stationary minimum<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4%2Fsqrt%287%29 ALIGN=MIDDLE  ALT=\"x=-4%2Fsqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> stationary maximum\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x%5E2+-+16%29%5E4 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x%5E2+-+16%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is\r<BR>\n" );
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document.write( "concave <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=up ALIGN=MIDDLE  ALT=\"up\"   DISABLED_style= \"max-width:90%; height:auto;\" >  on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-4%2Fsqrt%287%29 ALIGN=MIDDLE  ALT=\"x%3C-4%2Fsqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "concave <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=down ALIGN=MIDDLE  ALT=\"down\"   DISABLED_style= \"max-width:90%; height:auto;\" >  on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2Fsqrt%287%29%3Cx%3C4%2Fsqrt%287%29 ALIGN=MIDDLE  ALT=\"-4%2Fsqrt%287%29%3Cx%3C4%2Fsqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "concave <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=up ALIGN=MIDDLE  ALT=\"up\"   DISABLED_style= \"max-width:90%; height:auto;\" >  on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E4%2Fsqrt%287%29 ALIGN=MIDDLE  ALT=\"x%3E4%2Fsqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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