document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=63932>Question 63932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine the critical numbers and the critical points for each of the following functions:show all work\r<BR>\n" );
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document.write( "A)f(x)= x3 + 3x2 -33x -35\r<BR>\n" );
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document.write( "B) g(x)=x3 - 36x\r<BR>\n" );
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document.write( "C) h(x)= x3 -3x2 -40x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #44590 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=44590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> determine the critical numbers and the critical points for each of the following functions:show all work\r<BR>\n" );
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document.write( "A)f(x)= x^3 + 3x^2 -33x -35<BR>\n" );
document.write( "f'(x)=3x^2+6x-33<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=3%28x%5E2%2B2x-11%29 ALIGN=MIDDLE  ALT=\"0=3%28x%5E2%2B2x-11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F3=3%28x%5E2%2B2x-11%29%2F3 ALIGN=MIDDLE  ALT=\"0%2F3=3%28x%5E2%2B2x-11%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2%2B2x-11 ALIGN=MIDDLE  ALT=\"0=x%5E2%2B2x-11\"   DISABLED_style= \"max-width:90%; height:auto;\" >  We can't solve this by factoring, so use the quadratic formula:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a=1, b=2, c=-11<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%2B-sqrt%28%282%29%5E2-4%281%29%28-11%29%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x=%28-2%2B-sqrt%28%282%29%5E2-4%281%29%28-11%29%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%2B-sqrt%284%2B44%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-2%2B-sqrt%284%2B44%29%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=x=%28-2%2B-sqrt%2848%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-2%2B-sqrt%2848%29%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=x=%28-2%2B-sqrt%2816%29%2Asqrt%283%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-2%2B-sqrt%2816%29%2Asqrt%283%29%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=x=%28-2-4%2Asqrt%283%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-2-4%2Asqrt%283%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2%2B4%2Asqrt%283%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=-2%2B4%2Asqrt%283%29%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=x=-1-2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x=-1-2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2B2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x=1%2B2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "B) g(x)=x^3 - 36x<BR>\n" );
document.write( "g'(x)=3x^2-36<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=3x%5E2-36 ALIGN=MIDDLE  ALT=\"0=3x%5E2-36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B36=3x%5E2-36%2B36 ALIGN=MIDDLE  ALT=\"0%2B36=3x%5E2-36%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36=3x%5E2 ALIGN=MIDDLE  ALT=\"36=3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2F3=3x%5E2%2F3 ALIGN=MIDDLE  ALT=\"36%2F3=3x%5E2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12=x%5E2 ALIGN=MIDDLE  ALT=\"12=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+\-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812%29=sqrt%28x%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2812%29=sqrt%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+\-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29%2Asqrt%283%29=x ALIGN=MIDDLE  ALT=\"sqrt%284%29%2Asqrt%283%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+\-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%283%29=x ALIGN=MIDDLE  ALT=\"2%2Asqrt%283%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "C) h(x)= x^3 -3x^2 -40x<BR>\n" );
document.write( "h'(x)=3x^2-6x-40  <BR>\n" );
document.write( "0=3x^2-6x-40  use the quadratic formula again.<BR>\n" );
document.write( "a=3, b=-6, and c=-40<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-%28-6%29%2B-sqrt%28%28-6%29%5E2-4%283%29%28-40%29%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"x=%28-%28-6%29%2B-sqrt%28%28-6%29%5E2-4%283%29%28-40%29%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%286%2B-sqrt%2836%2B480%29%29%2F6 ALIGN=MIDDLE  ALT=\"x=%286%2B-sqrt%2836%2B480%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%286%2B-sqrt%28516%29%29%2F6 ALIGN=MIDDLE  ALT=\"x=%286%2B-sqrt%28516%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%286%2B-sqrt%284%29%2Asqrt%28129%29%29%2F6 ALIGN=MIDDLE  ALT=\"x=%286%2B-sqrt%284%29%2Asqrt%28129%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%286-2%2Asqrt%28129%29%29%2F6 ALIGN=MIDDLE  ALT=\"x=%286-2%2Asqrt%28129%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%286%2B2%2Asqrt%28129%29%29%2F6 ALIGN=MIDDLE  ALT=\"x=%286%2B2%2Asqrt%28129%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%283-sqrt%28129%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x=2%283-sqrt%28129%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%283%2Bsqrt%28129%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x=2%283%2Bsqrt%28129%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%283-sqrt%28129%29%29%2F3 ALIGN=MIDDLE  ALT=\"x=%283-sqrt%28129%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%283%2Bsqrt%28129%29%29%2F3 ALIGN=MIDDLE  ALT=\"x=%283%2Bsqrt%28129%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Happy Calculating!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );