document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=993482>Question 993482</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the function <BR>\n" );
document.write( "y = ( x - 4 ) ( x^2 + 3x + 2 )<BR>\n" );
document.write( "find the coordinates of the two stationary points and the point of inflection. \r<BR>\n" );
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document.write( "Note.   A stationary point is a critical point at which the derivative is 0. \r<BR>\n" );
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document.write( "Please enter your answer as a list of coordinate pairs, where a single coordinate pair (a, b) \r<BR>\n" );
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document.write( "THANK YOU  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #612739 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=612739\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "In order to find the stationary points, you need to find the zeros of the first derivative.  In order to find the point of inflection you will need to find the zero of the second derivative. None of this is very rigorous, but will work just fine for a polynomial function.\r<BR>\n" );
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document.write( "You have two choices for finding the first derivative.  Since you have the product of two functions, you can use the product rule:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(x)\ =\ f(x)g(x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{dx}h(x)\ =\ f(x)g'(x)\ +\ f'(x)g(x)\">\r<BR>\n" );
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document.write( "Or you can just perform the indicated multiplication and take the derivative by repeated applications of the power rule.\r<BR>\n" );
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document.write( "Either way, after you have the first derivative, set the quadratic equal to zero and solve.  You will get the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> values of the two stationary points.\r<BR>\n" );
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document.write( "The second derivative is just the derivative of the first derivative quadratic polynomial\r<BR>\n" );
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document.write( "Set the second derivative equal to zero and solve for the value of the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> coordinate of the inflection point.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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