What Are Tangent and Normal Lines?
Tangent Line: A straight line that touches a curve at exactly one point (the point of tangency) and has the same slope as the curve at that point. It represents the instantaneous rate of change of the function.
Normal Line: A straight line that is perpendicular to the tangent line at the point of tangency. It meets the curve at a right angle at that point.
Think of a tangent line as the line a car would follow if it suddenly lost all steering at a given moment on a curved road , it captures the exact direction of travel at that instant.
Note
The tangent and normal lines at a point are always perpendicular to each other. This means if you know one, you can immediately find the other using the negative reciprocal relationship for slopes.