document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=25761>Question 25761</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me with this, we are doing differential Calculus.<BR>\n" );
document.write( "Find the equation of the tangetn for each given x-value.<BR>\n" );
document.write( "y=x^2+8x+12, where x = -4.<BR>\n" );
document.write( "At the back of the book, it says the answer is y=-4<BR>\n" );
document.write( "I have no idea how to get that.<BR>\n" );
document.write( "thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #13875 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=13875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> As you probably know, the slope of the tangent at the given point (x = -4) is given by the value of the 1st derivative of the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2%2B8x%2B12 ALIGN=MIDDLE  ALT=\"y+=+x%5E2%2B8x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > at that point (x = -4).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx+=+2x+%2B+8 ALIGN=MIDDLE  ALT=\"dy%2Fdx+=+2x+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute x = -4 and solve.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx+=+2%28-4%29+%2B+8 ALIGN=MIDDLE  ALT=\"dy%2Fdx+=+2%28-4%29+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx+=+0 ALIGN=MIDDLE  ALT=\"dy%2Fdx+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > So, the slope of the tangent is 0 which means that it's a horizontal line. To find the point (x, y) of tangency, you'll substitute x = -4 into the original equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-4%29%5E2+%2B+8%28-4%29+%2B+12 ALIGN=MIDDLE  ALT=\"y+=+%28-4%29%5E2+%2B+8%28-4%29+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+16+-+32+%2B+12 ALIGN=MIDDLE  ALT=\"y+=+16+-+32+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-4 ALIGN=MIDDLE  ALT=\"y+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The point of tangency is (-4, -4) and the equation of the line passing through that point with a slope of m = 0 is:<BR>\n" );
document.write( " Using the point-slope form:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y1+=+m%28x-x1%29 ALIGN=MIDDLE  ALT=\"y-y1+=+m%28x-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-%28-4%29+=+0%28x-%28-4%29%29 ALIGN=MIDDLE  ALT=\"y+-%28-4%29+=+0%28x-%28-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%2B+4+=+0 ALIGN=MIDDLE  ALT=\"y+%2B+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-4 ALIGN=MIDDLE  ALT=\"y+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the equation of the tangent at x = -4\r<BR>\n" );
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document.write( "Here's what it looks like in a graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C2%2C-6%2C5%2Cx%5E2%2B8x%2B12%2C-4%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C2%2C-6%2C5%2Cx%5E2%2B8x%2B12%2C-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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