document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=996088>Question 996088</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let g(x) = x |x + 5|\r<BR>\n" );
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document.write( "Find all critical numbers (if any) of g. Give answers in increasing order. Enter DNE in any unused space(s).\r<BR>\n" );
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document.write( "x =  <BR>\n" );
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document.write( "x = \r<BR>\n" );
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document.write( "Please help I dont understand the whole set up of absolute value. I had someone help solve and got.<BR>\n" );
document.write( "g(x) = x|x+5| <BR>\n" );
document.write( "|x+5| = (x+5) for x &#8805; -5 <BR>\n" );
document.write( "|x+5| = -(x+5) for x < -5 \r<BR>\n" );
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document.write( "I don't understand this at all. Why is it &#8805; or <\r<BR>\n" );
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document.write( "How is this solved..<BR>\n" );
document.write( "So confused<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 #614652 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=614652\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rule: if y = |x|, then dy/dx = |x|/x\r<BR>\n" );
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document.write( "Apply the derivative<BR>\n" );
document.write( "g(x) = x*|x+5|<BR>\n" );
document.write( "g ' (x) = |x+5| + x*(|x+5|)/(x+5) ... product rule (also use the rule above)<BR>\n" );
document.write( "g ' (x) = |x+5| * [1 + x/(x+5)]<BR>\n" );
document.write( "g ' (x) = |x+5| * [1*(x+5)/(x+5) + x/(x+5)]<BR>\n" );
document.write( "g ' (x) = |x+5| * [(x+5)/(x+5) + x/(x+5)]<BR>\n" );
document.write( "g ' (x) = |x+5| * [(x+5+x)/(x+5)]<BR>\n" );
document.write( "g ' (x) = |x+5|*(2x+5)/(x+5)\r<BR>\n" );
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document.write( "Solve g ' (x) = 0 for x to find the critical values<BR>\n" );
document.write( "g ' (x) = |x+5|*(2x+5)/(x+5)<BR>\n" );
document.write( "0 = |x+5|*(2x+5)/(x+5)<BR>\n" );
document.write( "|x+5| = 0 or (2x+5)/(x+5) = 0<BR>\n" );
document.write( "|x+5| = 0 or 2x+5 = 0\r<BR>\n" );
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document.write( "If |x+5| = 0, then x+5 = 0 and x = -5<BR>\n" );
document.write( "If 2x+5 = 0, then x = -5/2 = -2.5\r<BR>\n" );
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document.write( "The critical numbers are <font color=\"red\">-5 and -2.5</font> </SPAN>\n" );
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