Tangent and normal lines help mathematicians understand the behavior of curves at specific points.
A tangent line to a curve at a given point is the line through that point with slope equal to the curve's instantaneous rate of change there, if the derivative exists.
The tangent line has the same slope as the curve at the point of tangency, making it invaluable for understanding the instantaneous rate of change of a function.
The normal line is perpendicular to the tangent line at the point of tangency. It is perpendicular to the tangent direction at that point, giving the direction orthogonal to the curve there.
To find the equations of tangent and normal lines, we primarily use the concept of derivatives.
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