Tangents and Normals
Tangents
A tangent is the linear function at a given point on the curve. It is used to find the instantaneous rate of change of a curve at a certain point.
To find the gradient of the tangent, substitute the given x-value into the derivative.
Normals
A normal is the linear function perpendicular to the tangent at any given point on the curve.
To find the equation of a normal, use the perpendicular gradient formula () to find .
Example:
To find the equation to the normal:
(1) Find the tangent gradient.(2) Find the normal function.