document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=397766>Question 397766</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hai sir, please help me on this problem\r<BR>\n" );
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document.write( "\"Determine all inflection points of function f defined by, f(x)  =  x4 + x3 + 2<BR>\n" );
document.write( "a)(0,1) and (1/2, 15/31)<BR>\n" );
document.write( " b)(0,1) and (1/3, 12/32)<BR>\n" );
document.write( " c)(0, 2) and ( -1/2, 31/16)<BR>\n" );
document.write( " d)None of these </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #281820 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=281820\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%2Fdx++=4x%5E3+%2B+3x%5E2 ALIGN=MIDDLE  ALT=\"df%2Fdx++=4x%5E3+%2B+3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2f%2Fdx%5E2+=+12x%5E2+%2B+6x+ ALIGN=MIDDLE  ALT=\"d%5E2f%2Fdx%5E2+=+12x%5E2+%2B+6x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Set the 2nd derivative to 0:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2f%2Fdx%5E2+=+12x%5E2+%2B+6x++=+6x%282x+%2B+1%29+=+0 ALIGN=MIDDLE  ALT=\"d%5E2f%2Fdx%5E2+=+12x%5E2+%2B+6x++=+6x%282x+%2B+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> x = 0, -1/2.<BR>\n" );
document.write( "When x = -1, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2f%2Fdx%5E2+%3E+0 ALIGN=MIDDLE  ALT=\"d%5E2f%2Fdx%5E2+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "when x = -1/4, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2f%2Fdx%5E2+%3C+0 ALIGN=MIDDLE  ALT=\"d%5E2f%2Fdx%5E2+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <BR>\n" );
document.write( "when x = 1, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2f%2Fdx%5E2+%3E+0 ALIGN=MIDDLE  ALT=\"d%5E2f%2Fdx%5E2+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Therefore there are changes of concavity in the intervals (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >, -1/2), (-1/2, 0), and (0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >).  To find the y-coordinates, substitute x = 0 and x = -1/2 in to original function.\r<BR>\n" );
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document.write( "The answer is c. </SPAN>\n" );
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