document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190587>Question 1190587</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the tangent to f(x) = x^2 at the point where <BR>\n" );
document.write( "i. x= 1<BR>\n" );
document.write( "ii. x= 4\r<BR>\n" );
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document.write( "Please explain step-by-step! </SPAN>\n" );
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document.write( "Part i)\r<BR>\n" );
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document.write( "Use the power rule to get the derivative<BR>\n" );
document.write( "f(x) = x^2<BR>\n" );
document.write( "f ' (x) = 2x\r<BR>\n" );
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document.write( "The derivative function will directly determine the slope of the tangent line.\r<BR>\n" );
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document.write( "If x = 1, then<BR>\n" );
document.write( "f ' (x) = 2x<BR>\n" );
document.write( "f ' (1) = 2*1<BR>\n" );
document.write( "f ' (1) = 2<BR>\n" );
document.write( "The slope of the tangent is m = 2 when x = 1.\r<BR>\n" );
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document.write( "Plug x = 1 into the original function<BR>\n" );
document.write( "f(x) = x^2<BR>\n" );
document.write( "f(1) = 1^2<BR>\n" );
document.write( "f(1) = 1<BR>\n" );
document.write( "The point (1,1) is on the f(x) curve.\r<BR>\n" );
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document.write( "Now apply the point-slope form<BR>\n" );
document.write( "y - y1 = m(x - x1)<BR>\n" );
document.write( "y - 1 = 2(x - 1)<BR>\n" );
document.write( "y - 1 = 2x - 2<BR>\n" );
document.write( "y = 2x-2+1<BR>\n" );
document.write( "y = 2x-1\r<BR>\n" );
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document.write( "The slope of the tangent line is <font color=red>y = 2x-1</font> when x = 1\r<BR>\n" );
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document.write( "----------------------------\r<BR>\n" );
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document.write( "For part ii), you'll follow very similar steps.\r<BR>\n" );
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document.write( "Use f ' (x) = 2x from earlier.\r<BR>\n" );
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document.write( "You should get a tangent slope of m = 8 and the point (4,16) is on the parabola.\r<BR>\n" );
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document.write( "The equation of the tangent line is <font color=red>y = 8x-16</font> when x = 4. <BR>\n" );
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