document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=666619>Question 666619</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 11-	Show work, for the function f(x)=x³+x, find the average rate of change of f from 1 to x:\r<BR>\n" );
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document.write( "a-	x³+x+2<BR>\n" );
document.write( "    x-1\r<BR>\n" );
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document.write( "b-	x²+x+2\r<BR>\n" );
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document.write( "c-	x²+2\r<BR>\n" );
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document.write( "d-	1<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 #414576 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=414576\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Average rate of change from a to b  of f(x):   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%28b%29-f%28a%29%29%2F%28b-a%29 ALIGN=MIDDLE  ALT=\"%28f%28b%29-f%28a%29%29%2F%28b-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%28x%29+-+f%281%29%29%2F%28x-1%29+=+%28x%5E3+%2B+x+-+2%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"%28f%28x%29+-+f%281%29%29%2F%28x-1%29+=+%28x%5E3+%2B+x+-+2%29%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use long division to arrive at the result:  \r<BR>\n" );
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document.write( "x-1 |  x^3+x-2\r<BR>\n" );
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document.write( "x goes into x^3 x^2 times\r<BR>\n" );
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document.write( "(x-1)x^2 = x^3 - x^2\r<BR>\n" );
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document.write( "x^2+x-2 is what's left.\r<BR>\n" );
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document.write( "x-1 | x^2 +x -2\r<BR>\n" );
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document.write( "x goes into x^2 x times\r<BR>\n" );
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document.write( "(x-1) * x = x^2-x\r<BR>\n" );
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document.write( "2x -2 is whats left.\r<BR>\n" );
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document.write( "x goes into 2x  2 times.\r<BR>\n" );
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document.write( "2*(x-1) = 2x-2\r<BR>\n" );
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document.write( "So there's nothing left (remainder of 0)\r<BR>\n" );
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document.write( "giving us x^2+x+2\r<BR>\n" );
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document.write( "x^2+x+2. Choice B </SPAN>\n" );
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