document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118506>Question 1118506</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a) use the method of first principal of differentiation to find the derivative of    y=f(x)= 9x-x^3.  hence find the equation of the tangent line to the curve y= f(x)at x= 1\r<BR>\n" );
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document.write( "(b)  find another point (x,y)on the curve y=f(x)=9x-x^3 where the tangent is parallel to the tangent in (a)above </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733870 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=733870\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \lim_{\delta x\right 0}\,\frac{f(x\,+\,\delta x)\ -\ f(x)}{\delta x}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \lim_{\delta x\right 0}\,\frac{\[9(x\,+\,\delta x)\,-\,(x\,+\,\delta x)^3\]\ -\ \[9x\,-\,x^3\]}{\delta x}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \lim_{\delta x\right 0}\,\frac{9x\,+\,9\delta x\,-\,x^3\,-\,3x^2\delta x\,-\,3x\delta x^2\,-\,\delta x^3\,-\,9x\,+\,x^3}{\delta x}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \lim_{\delta x\right 0}\,\frac{9\delta x\,-\,3x^2\delta x\,-\,3x\delta x^2\,-\,\delta x^3}{\delta x}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \lim_{\delta x\right 0}\,9\,-\,3x^2\,-\,3x\delta x\,-\delta x^2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ 9\,-\,3x^2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(1)\ =\ 9(1)\ -\ 1^3\ =\ 8\">\r<BR>\n" );
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document.write( "Slope of tangent at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (1,\,8)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\|_{x=1}\ =\ 9\ -\ 3(1)^2\ =\ 6\">\r<BR>\n" );
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document.write( "Point-Slope form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  y\ -\ 8\ =\ 6(x\ -\ 1)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  y\ =\ 6x\ +\ 2\">\r<BR>\n" );
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document.write( "Part B:\r<BR>\n" );
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document.write( "The slopes of parallel lines are equal.  Hence, you need to find another value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> such that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 9\ -\ 3x^2\ =\ 6\">.  We already know that one of the roots of this equation is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 1\">.  Find the other.  Then find the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(-1)\">.  Then derive an equation of the line that passes through the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \(x,\,f(-1)\)\"> with a slope of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 6\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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