AP Calculus AB and BC glossary

Normal line

The normal line at a point on a curve is the line through that point perpendicular to the tangent line. Its slope is the negative reciprocal of the derivative there, provided the derivative is not zero.

y−f(a)=−1f′(a)(x−a)y - f(a) = -\frac{1}{f'(a)}(x - a)

Everything about the tangent line carries over except the slope, which flips and changes sign. If the tangent slope is 23\frac{2}{3}, the normal slope is −32-\frac{3}{2}.

Two special cases

If f′(a)=0f'(a) = 0 the tangent is horizontal, so the normal line is vertical with equation x=ax = a. If the tangent is vertical, the normal line is horizontal.

Appears in: Unit 2: Defining the Derivative