SOLUTION: Stuck on question 3 which is about equation of the tangent! Curve c has equation y=2x^2+6x+7. The ponit p, whose co-ordinates is -1,lies on the curve c. Find the equation of the t

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Question 747753: Stuck on question 3 which is about equation of the tangent!
Curve c has equation y=2x^2+6x+7. The ponit p, whose co-ordinates is -1,lies on the curve c. Find the equation of the tangent to C at P.
Explained answer as i dont get this type of question.
Answer by Cromlix(4381) (Show Source):
You can put this solution on YOUR website!
The point P's coordinate -1 is the x coordinate.
Assuming it is, substitute -1 into the equation
y = 2x^2 + 6x + 7 to find the 'y' value.
y = 2(-1)^2 + 6(-1) + 7
y = 2 + (-6) + 7
y = 3 So P's coords are (-1, 3)
Next differentiate 2x^2 + 6x + 7
dy/dx = 4x + 6
Substitute x = -1 into the differentiated equation
= 4(-1) + 6 = 2 This is the gradient(m)
at point P.
Using y - b = m(x - a)
Substitute P's x and y coords (x = a and y = b)
y - 3 = 2(x + 1)
y - 3 = 2x + 2
y = 2x + 2 + 3
y = 2x + 5 This is the equation of the tangent at P
Hope this helps