Tangents and Normals (1 Viewer)

[Arithela]

1. Find the coordinates of the point on the curve y = x^2 at which the tangent is parallel to the line 2x - y + 1 = 0.

2. Find the coordinates of the point on the curve y = x^3 - x at which the gradient of the tangents is 11.

3. Find the coordinates of the point on the curve y = 2x^2 - 4x + 3 at which the normal to the curive is parallel to the line x + 4y + 2 = 0

Can somebody show me how to do these types of questions?

 

[Mattamz]

The method for all three questions is the same: For (1):

Rearranging 2x - y + 1 = 0:
y = 2x + 1
Gradient = 2

diff. y = x^2:
dy/dx = 2x

therefore:
2x = 2
x =1

ie at x=1 the tangent is parralel to 2x- y +1 = 0

 

[Arithela]

got it, thank u

 

[zingerburger]

Damn it, Tam. Save some questions for me.