document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058087>Question 1058087</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Having trouble with the multiplicities concept:\r<BR>\n" );
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document.write( "State the multiplicity of each of the zeros found in part (c). Describe how the multiplicity affects the behavior of the given function’s graph at each of these zeros.\r<BR>\n" );
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document.write( "What I have:\r<BR>\n" );
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document.write( "Original equation: f(x)=x^3-3x^2\r<BR>\n" );
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document.write( "I found the zeros after factoring the equation to: x^2(x-3)\r<BR>\n" );
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document.write( "Zeros of X are: (0,0) and (3,0)\r<BR>\n" );
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document.write( "I'm having a problem relating this to the multiplicities- any help would be greatly appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673098 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=673098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are pretty much on the right track.\r<BR>\n" );
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document.write( "So the zeros are:<BR>\n" );
document.write( "0  (multiplicity 2)<BR>\n" );
document.write( "3  (multiplicity 1)\r<BR>\n" );
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document.write( "The higher the multiplicity of a zero, the flatter the function is near that zero.   This is easy to see using Calculus:  for multiplicity of  2 or more, the derivative of f(x) (= rate of change of f(x)) will also have that zero.  \r<BR>\n" );
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