document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187895>Question 1187895</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the gradient of f(x) at x=4 for which f(x)=(5(x-1)(x-5))/8x^1/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819001 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=819001\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Find the gradient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > for which <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%285%28x-1%29%28x-5%29%29%2F%288x%5E%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%285%28x-1%29%28x-5%29%29%2F%288x%5E%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%285%28x-1%29%28x-5%29%29%2F%288sqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%285%28x-1%29%28x-5%29%29%2F%288sqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "The gradient (slope) of a curve of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=a+ ALIGN=MIDDLE  ALT=\"x=a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%29 ALIGN=MIDDLE  ALT=\"%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "By taking the derivative, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29%28%285+%28x+-+1%29+%28x+-+5%29%29%2F%288sqrt%28x%29%29%29+we+get+%0D%0A%0D%0A%0D%0A%7B%7B%7Bf ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29+=+%285+%283+x%5E2+-+6+x+-+5%29%29%2F%2816+x%5E%283%2F2%29%29 ALIGN=MIDDLE  ALT=\"%28x%29+=+%285+%283+x%5E2+-+6+x+-+5%29%29%2F%2816+x%5E%283%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "By plugging in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29+=+%285+%283%2A4%5E2+-+6%2A4+-+5%29%29%2F%2816%2A4%5E%283%2F2%29%29 ALIGN=MIDDLE  ALT=\"%284%29+=+%285+%283%2A4%5E2+-+6%2A4+-+5%29%29%2F%2816%2A4%5E%283%2F2%29%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=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29+=+95%2F128 ALIGN=MIDDLE  ALT=\"%284%29+=+95%2F128\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hence, the gradient is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=95%2F128+ ALIGN=MIDDLE  ALT=\"95%2F128+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (exact solution) approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.7421875 ALIGN=MIDDLE  ALT=\"0.7421875\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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