document.write( "Question 450127: The curve C has equation y=2x2 +6x +7. the point, whose x-coordinate is -1, lies on the curve c. Find the equation of the tangent to C at P \n" ); document.write( "

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The curve C has equation y=2x2 +6x +7. the point, whose x-coordinate is -1, lies on the curve c. Find the equation of the tangent to C at P
\n" ); document.write( "The derivative of the curve at any point will give us the slope of the tangent line at that point.
\n" ); document.write( "dy/dx = 4x + 6
\n" ); document.write( "The x-coordinate of point P is -1. Insert this in the above equation:
\n" ); document.write( "dy/dx = 4(-1) + 6 = 2
\n" ); document.write( "The y-value is given from the original curve:
\n" ); document.write( "y = 2(-1)^2 + 6(-1) + 7 = 3
\n" ); document.write( "So the coordinates of point P are (-1,3)
\n" ); document.write( "Now we have the slope and a point on the line. Use the coordinates of the point
\n" ); document.write( "to get the y-intercept:
\n" ); document.write( "y = mx + b -> y1 = mx1 + b -> 3 = 2(-1) + b -> b = 5
\n" ); document.write( "Therefore, the equation of the line is:
\n" ); document.write( "y = 2x + 5 \n" ); document.write( "

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