document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=291563>Question 291563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the k values such that y= 4x + k does not intersect the parbola y=-3x^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 #210782 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=210782\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Take the first derivative of your parabola function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y'\ =\ -6x\ -\ 1\">\r<BR>\n" );
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document.write( "The slope of the line is 4, so set the derivative function equal to that slope:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -6x\ -\ 1\ =\ 4\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ -\frac{5}{6}\">\r<BR>\n" );
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document.write( "If the line were actually tangent, then the point of tangency would be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(-\frac{5}{6},f\left(-\frac{5}{6}\right)\right)\">\r<BR>\n" );
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document.write( "Do the arithmetic:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -3\left(-\frac{5}{6}\right)^2\ -\ \left(-\frac{5}{6}\right)\ +\ 4\ =\ \frac{11}{4}\">\r<BR>\n" );
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document.write( "So, for a tangent line:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{11}{4}\ =\ 4\left(-\frac{5}{6}\right)\ +\ k\">\r<BR>\n" );
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document.write( "Hence,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ k\ =\ \frac{73}{12}\">\r<BR>\n" );
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document.write( "So, if the line must not intersect the parabola:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ k\ >\ \frac{73}{12}\">  </SPAN>\n" );
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