SOLUTION: 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

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
RELATED QUESTIONS
Stuck on question 3 which is about equation of the tangent! Curve c has equation... (answered by Cromlix)

The curve whose equation is y= (2x2+3s-9)(x-k), where k is a constant, has a turning... (answered by Greenfinch)

Find an equation of the tangent line to the curve y=e^x/(1+2e^x ) at the point whose... (answered by MathLover1)

Obtain the equation of the curve y=ax^2+bx+c,using the following conditions (i)... (answered by Fombitz)

The curve y=ax�+bx+c passes (2,5), (3,12) and (-1,-4). Find the equation of the... (answered by MathLover1)

In a figure, curve A whose equation is y=(x+a)^2, passes through the point (4,0). Curve... (answered by Boreal)

what is the y-coordinate for the point on the curve with x-coordinate... (answered by asuar010)

curve c is described by the equation 0.25x2+y2=9. determine the y coordinates of the... (answered by solver91311)

determine the equation of the curve such that the sum of the distance of any point on the (answered by ikleyn)