document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=824097>Question 824097</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that f(x)= x^3-x+1, find (f(h)-f(-h))/2h<BR>\n" );
document.write( "Thanks!!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #496080 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=496080\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)= x^3-x+1\r<BR>\n" );
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document.write( "f(h)= h^3-h+1 ... replace EVERY copy of x with h\r<BR>\n" );
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document.write( "f(x)= x^3-x+1\r<BR>\n" );
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document.write( "f(-h)= (-h)^3-(-h)+1 ... replace EVERY copy of x with -h\r<BR>\n" );
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document.write( "f(-h)= -h^3-(-h)+1\r<BR>\n" );
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document.write( "f(-h)= -h^3+h+1\r<BR>\n" );
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document.write( "f(h)-f(-h) = (h^3-h+1) - (-h^3+h+1)\r<BR>\n" );
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document.write( "f(h)-f(-h) = h^3-h+1 + h^3 - h - 1\r<BR>\n" );
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document.write( "f(h)-f(-h) = 2h^3-2h\r<BR>\n" );
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document.write( "So...\r<BR>\n" );
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document.write( "(f(h)-f(-h))/2h\r<BR>\n" );
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document.write( "turns into\r<BR>\n" );
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document.write( "(2h^3-2h)/2h\r<BR>\n" );
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document.write( "then you factor out 2h in the numerator to get\r<BR>\n" );
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document.write( "(2h(h^2-1))/2h\r<BR>\n" );
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document.write( "and then cancel out the '2h' terms to get\r<BR>\n" );
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document.write( "h^2 - 1\r<BR>\n" );
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document.write( "and then you can optionally factor to get\r<BR>\n" );
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document.write( "(h-1)(h+1)\r<BR>\n" );
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document.write( "So the answer is either <font color=\"red\">h^2 - 1</font> or <font color=\"red\">(h-1)(h+1)</font>\r<BR>\n" );
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document.write( "They are equivalent. The second expression is the factored form of the first (using the difference of squares rule). </SPAN>\n" );
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