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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
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! 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
The derivative of the curve at any point will give us the slope of the tangent line at that point.
dy/dx = 4x + 6
The x-coordinate of point P is -1. Insert this in the above equation:
dy/dx = 4(-1) + 6 = 2
The y-value is given from the original curve:
y = 2(-1)^2 + 6(-1) + 7 = 3
So the coordinates of point P are (-1,3)
Now we have the slope and a point on the line. Use the coordinates of the point
to get the y-intercept:
y = mx + b -> y1 = mx1 + b -> 3 = 2(-1) + b -> b = 5
Therefore, the equation of the line is:
y = 2x + 5
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