document.write( "Question 1121247: Answer Checking:\r
\n" ); document.write( "\n" ); document.write( "What is the slope of the tangent line through (0,-3) and (x,y) for y = 3x² - 3
\n" ); document.write( "and x=1?\r
\n" ); document.write( "\n" ); document.write( "my answer is m=3x^2
\n" ); document.write( "but i think their looking for non variable answer \n" ); document.write( "
Algebra.Com's Answer #737047 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
What is the slope of the tangent line through (0,-3) and (x,y)
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document.write( "It's best to draw a graph when you can.\r\n" );
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document.write( "You want the slope of the green tangent line which goes through at (0,-3)\r\n" );
document.write( "and the blue tangent line which is through the point where x=1, which has\r\n" );
document.write( "the y-value found by substituting 1 for x in y = 3x² - 3\r\n" );
document.write( "                        y = 3(1)² - 3\r\n" );
document.write( "                        y = 3(1) - 3\r\n" );
document.write( "                        y = 3 - 3\r\n" );
document.write( "                        y = 0\r\n" );
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document.write( "So the blue line goes through the point (1,0). \r\n" );
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document.write( "The derivative is a formula for finding the slope of a tangent line at any\r\n" );
document.write( "point.   So we find the derivative:\r\n" );
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document.write( "                       y = 3x² - 3\r\n" );
document.write( "                      y' = 6x\r\n" );
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document.write( "To find the slope of the green tangent line, we substitute the x value of\r\n" );
document.write( "the point (0,-3), which is 0, in the derivative:\r\n" );
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document.write( "                      y' = 6(0)\r\n" );
document.write( "                      y' = 0\r\n" );
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document.write( "So the slope of the green tangent line is 0. [You expect that because the green\r\n" );
document.write( "line is horizontal, and any horizontal line has slope 0.\r\n" );
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document.write( "To find the slope of the blue tangent line, we substitute the x value of the\r\n" );
document.write( "point (1,0), which is 1, in the derivative:\r\n" );
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document.write( "                      y' = 6(1)\r\n" );
document.write( "                      y' = 6\r\n" );
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document.write( "So the slope of the blue tangent line is 6.  The blue line goes up to the right\r\n" );
document.write( "so we would expect it to have a positive number for its slope, and a slope of 6\r\n" );
document.write( "is pretty steep.\r\n" );
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document.write( "Edwin

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