document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180829>Question 1180829</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find x coordinate of the point on the graph y=square root of x+8 where the tangent line is parallel to the secant line that cuts the curve at x =-8 and x=7.  </SPAN>\n" );
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document.write( "Evaluate the function at x=-8 and x=7: f(-8)=0; f(7)=sqrt(15).<br><BR>\n" );
document.write( "Find the equation of the secant: (-8,0) to (7,sqrt(15))<br><BR>\n" );
document.write( "slope = sqrt(15)/(7-(-8)) = sqrt(15)/15<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-0=%28sqrt%2815%29%2F15%29%28x%2B8%29 ALIGN=MIDDLE  ALT=\"y-0=%28sqrt%2815%29%2F15%29%28x%2B8%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+=+%281%2Fsqrt%2815%29%29%28x%2B8%29 ALIGN=MIDDLE  ALT=\"y+=+%281%2Fsqrt%2815%29%29%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Graph the function and the secant:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-2%2C5%2Csqrt%28x%2B8%29%2C%281%2Fsqrt%2815%29%29%28x%2B8%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Find the derivative of the function:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%2B8%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"y+=+%28x%2B8%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx+=+%281%2F2%29%28%28x%2B8%29%5E%28-1%2F2%29%29%281%29+=+1%2F%282sqrt%28x%2B8%29%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx+=+%281%2F2%29%28%28x%2B8%29%5E%28-1%2F2%29%29%281%29+=+1%2F%282sqrt%28x%2B8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Find the x value where the slope of the tangent is the same as the slope of the secant.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%282sqrt%28x%2B8%29%29%29=1%2Fsqrt%2815%29 ALIGN=MIDDLE  ALT=\"%281%2F%282sqrt%28x%2B8%29%29%29=1%2Fsqrt%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%28x%2B8%29=sqrt%2815%29 ALIGN=MIDDLE  ALT=\"2sqrt%28x%2B8%29=sqrt%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%2B8%29=15 ALIGN=MIDDLE  ALT=\"4%28x%2B8%29=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B32=15 ALIGN=MIDDLE  ALT=\"4x%2B32=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=-17 ALIGN=MIDDLE  ALT=\"4x=-17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-17%2F4 ALIGN=MIDDLE  ALT=\"x=-17%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Graph the line with slope sqrt(15)/15 touching y=sqrt(x+8) at x=-17/4 and observe that it is parallel to the secant:<br><BR>\n" );
document.write( "Graph the function and the secant:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-2%2C5%2Csqrt%28x%2B8%29%2C%281%2Fsqrt%2815%29%29%28x%2B8%29%2C%281%2Fsqrt%2815%29%29%28x%2B17%2F4%29%2Bsqrt%2815%29%2F2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: x = -17/4.<br><BR>\n" );
document.write( "At x=-17/4, the tangent to y=sqrt(x+8) is parallel to the secant through x=-8 and x=7.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );