document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=560133>Question 560133</A>: <I><SPAN STYLE=\"word-break: break-all;\"> F(x) = 4x^3 - 5x 2x^(1/2). Determine the slope of the tangent when 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 #363702 by </B><A HREF=/tutors/aboutme.mpl?userid=nyc_function><B>nyc_function(2741)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nyc_function><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=nyc_function><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=363702\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a calculus 1 question.\r<BR>\n" );
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document.write( "You need to find the derivative of F(x).\r<BR>\n" );
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document.write( "I'm looking for F'(x).  So, I will do this by differenting termwise.\r<BR>\n" );
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document.write( "(4x^3)' = 12x^2\r<BR>\n" );
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document.write( "(-5x)' = -5\r<BR>\n" );
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document.write( "(2x^1/2)' = x^(-1/2)\r<BR>\n" );
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document.write( "We can write  x^(-1/2) as 1/sqrt{x}.\r<BR>\n" );
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document.write( "So, F'(x) = 12x^2 + 1/sqrt{x} - 5\r<BR>\n" );
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document.write( "To find the slope of the tangent line, we now replace every x you see with 4 and simplify.\r<BR>\n" );
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document.write( "F'(4) = 12(4)^2 + 1/sqrt{4} - 5\r<BR>\n" );
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document.write( "F'(4) = 12*16 + 1/2 - 5\r<BR>\n" );
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document.write( "F'(4) = 375/2\r<BR>\n" );
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document.write( "The slope of the tangent line is 375/2.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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