document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087244>Question 1087244</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(x)= 2x^3 - x, find [f(x+h)-f(x)]/h\r<BR>\n" );
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document.write( "Please, i'm stuck. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #701517 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=701517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">The first thing we need to do is find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We do this by replacing every copy of x with x+h\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28highlight%28x%29%29=+2%28highlight%28x%29%29%5E3+-+%28highlight%28x%29%29 ALIGN=MIDDLE  ALT=\"f%28highlight%28x%29%29=+2%28highlight%28x%29%29%5E3+-+%28highlight%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Highlighting the x terms we will replace\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28highlight%28x%2Bh%29%29=+2%28highlight%28x%2Bh%29%29%5E3+-+%28highlight%28x%2Bh%29%29 ALIGN=MIDDLE  ALT=\"f%28highlight%28x%2Bh%29%29=+2%28highlight%28x%2Bh%29%29%5E3+-+%28highlight%28x%2Bh%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replacing those terms with x+h\r<BR>\n" );
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document.write( "So we have\r<BR>\n" );
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document.write( "Let's expand that out and simplify\r<BR>\n" );
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document.write( "Now we can compute the difference quotient\r<BR>\n" );
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document.write( "So the final answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+6x%5E2%2B6xh%2B2h%5E2+-+1 ALIGN=MIDDLE  ALT=\"%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+6x%5E2%2B6xh%2B2h%5E2+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Side Note: After this step is reached, you can plug in h = 0 to find the derivative of f(x). This topic probably hasn't come up yet in your course, but it definitely will come up in calculus. </font> </SPAN>\n" );
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