document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040330>Question 1040330</A>: <I><SPAN STYLE=\"word-break: break-all;\"> F(x+h)-f(x)/h where f(x)=x^2-x+4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655131 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=655131\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's start by computing f(x+h)\r<BR>\n" );
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document.write( "f(x) = x^2 - x + 4<BR>\n" );
document.write( "f(x+h) = (x+h)^2 - (x+h) + 4 ... replace every 'x' with (x+h)<BR>\n" );
document.write( "f(x+h) = (x^2+2xh+h^2) - (x+h) + 4<BR>\n" );
document.write( "f(x+h) = x^2+2xh+h^2 - x-h + 4\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29+=+x%5E2%2B2xh%2Bh%5E2+-+x-h+%2B+4 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29+=+x%5E2%2B2xh%2Bh%5E2+-+x-h+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "----------------------------\r<BR>\n" );
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document.write( "Using what we found earlier, let's subtract f(x) from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29+=+x%5E2%2B2xh%2Bh%5E2+-+x-h+%2B+4 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29+=+x%5E2%2B2xh%2Bh%5E2+-+x-h+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29-f%28x%29+=+x%5E2%2B2xh%2Bh%5E2+-+x-h+%2B+4-f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29-f%28x%29+=+x%5E2%2B2xh%2Bh%5E2+-+x-h+%2B+4-f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29-f%28x%29+=+x%5E2%2B2xh%2Bh%5E2+-+x-h+%2B+4-%28f%28x%29%29 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29-f%28x%29+=+x%5E2%2B2xh%2Bh%5E2+-+x-h+%2B+4-%28f%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29-f%28x%29+=+x%5E2%2B2xh%2Bh%5E2+-+x-h+%2B+4-%28x%5E2-x%2B4%29 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29-f%28x%29+=+x%5E2%2B2xh%2Bh%5E2+-+x-h+%2B+4-%28x%5E2-x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace f(x) with x^2-x+4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29-f%28x%29+=+x%5E2%2B2xh%2Bh%5E2+-+x-h+%2B+4-x%5E2%2Bx-4 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29-f%28x%29+=+x%5E2%2B2xh%2Bh%5E2+-+x-h+%2B+4-x%5E2%2Bx-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29-f%28x%29+=+2xh%2Bh%5E2-h ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29-f%28x%29+=+2xh%2Bh%5E2-h\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "----------------------------<BR>\n" );
document.write( "Now that's divide that by h\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29-f%28x%29+=+2xh%2Bh%5E2-h ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29-f%28x%29+=+2xh%2Bh%5E2-h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%282xh%2Bh%5E2-h%29%2Fh ALIGN=MIDDLE  ALT=\"%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%282xh%2Bh%5E2-h%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%28h%282x%2Bh-1%29%29%2Fh ALIGN=MIDDLE  ALT=\"%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%28h%282x%2Bh-1%29%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+2x%2Bh-1 ALIGN=MIDDLE  ALT=\"%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+2x%2Bh-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------\r<BR>\n" );
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document.write( "So in the end, after simplifying, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%28x%2Bh%29-f%28x%29%29%2Fh ALIGN=MIDDLE  ALT=\"%28f%28x%2Bh%29-f%28x%29%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2Bh-1 ALIGN=MIDDLE  ALT=\"2x%2Bh-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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