document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=556891>Question 556891</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the abscissae of the maxima, minima and inflection points. <BR>\n" );
document.write( "y = x^4 + 6x^3 - 5 <BR>\n" );
document.write( "The answer is supposed to be: Minimum at x point = -9/2, inflection points at x=0 and x=-3 <BR>\n" );
document.write( "I don't know how to do this, help me please.<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 #362517 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=362517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Take the first derivative and set it equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{dy}{dx} = 4x^3 + 18x^2 = 0\">\r<BR>\n" );
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document.write( "This equals zero at x = 0 and x = -9/2. Now take the second derivative and set it to zero to find possible inflection points:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{d^2y}{dx^2} = 12x^2 + 36x = 0\">\r<BR>\n" );
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document.write( "x = 0 and x = -3 are the x-coordinates for possible inflection points. Note that you still have to test these points for concavity, as the concavity does not always change when the second derivative equals zero. </SPAN>\n" );
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