document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1048785>Question 1048785</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the Equation of a Tangent Line to f(x) = 3x^2 - 11x + 23 at the point (1,15)\r<BR>\n" );
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document.write( "I've worked out using the 1st derivative as hinted and would appreciate any checking if this is correct, many thanks.\r<BR>\n" );
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document.write( "1st derivative: d/dx [f(x)]<BR>\n" );
document.write( "f'(x)= d/dx [3x^2 - 11x + 23]<BR>\n" );
document.write( "=3* d/dx [x^2] - 11* d/dx [x] + d/dx [23]  (using power rule)<BR>\n" );
document.write( "=3*2x - 11*1 + 0<BR>\n" );
document.write( "=6x - 11\r<BR>\n" );
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document.write( "Plug x=1 into f'(x)<BR>\n" );
document.write( "f'(1) = 6(1) - 11<BR>\n" );
document.write( "= -5\r<BR>\n" );
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document.write( "Using point-slope form<BR>\n" );
document.write( "y-y1 = m(x-x1)<BR>\n" );
document.write( "y-15 = -5(x-1)<BR>\n" );
document.write( "y=-5x+5+15<BR>\n" );
document.write( "Ans: y=-5x+20<BR>\n" );
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