document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192428>Question 1192428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The graph of y = 2x^3 + ax^2 + b has a stationary point (-3,19) . Find the value of a and b. Determine the nature of the stationary point (-3,19). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824480 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=824480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E3%2Bax%5E2%2Bb ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E3%2Bax%5E2%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=19 ALIGN=MIDDLE  ALT=\"f%28-3%29=19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-54%2B9a%2Bb=19 ALIGN=MIDDLE  ALT=\"-54%2B9a%2Bb=19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%2Fdx=6x%5E2%2B2ax ALIGN=MIDDLE  ALT=\"df%2Fdx=6x%5E2%2B2ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The stationary point at x=-3 is where the derivative is zero.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B2ax=54-6a=0 ALIGN=MIDDLE  ALT=\"6x%5E2%2B2ax=54-6a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=9 ALIGN=MIDDLE  ALT=\"a=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use that value of a to solve for b.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-54%2B9%289%29%2Bb=19 ALIGN=MIDDLE  ALT=\"-54%2B9%289%29%2Bb=19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27%2Bb=19 ALIGN=MIDDLE  ALT=\"27%2Bb=19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-8 ALIGN=MIDDLE  ALT=\"b=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3%2B9x%5E2-8 ALIGN=MIDDLE  ALT=\"2x%5E3%2B9x%5E2-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We know f(-3)=19; and f(0)=-8.  Those two points, along with the positive leading coefficient, tell us that the stationary point at (-3,19) is a local maximum.<br><BR>\n" );
document.write( "Or, more formally, to show that the stationary point is a local maximum, we could find the second derivative of the function and show that it is negative at x=-3.<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "a=9<BR>\n" );
document.write( "b=-8<BR>\n" );
document.write( "(-3,19) is a local maximum<br><BR>\n" );
document.write( "A graph....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C3%2C-10%2C30%2C2x%5E3%2B9x%5E2-8%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C3%2C-10%2C30%2C2x%5E3%2B9x%5E2-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );