SL 5.4—Tangents and normals
- Syllabus
- First assessment 2021
- Objective
- —
- Level
- HL
A tangent uses the derivative; a normal uses its negative reciprocal
A tangent uses the derivative; a normal uses its negative reciprocal.
At x=a, the tangent slope is f′(a); a perpendicular normal has slope −1/f′(a) when the tangent is neither horizontal nor vertical.
Example
For y=x² at x=1, the tangent is y−1=2(x−1), while the normal is y−1=−(x−1)/2.
Find the point and tangent slope first, then use point–slope form for the requested line.
A vertical tangent has a horizontal normal, so the reciprocal-slope formula needs a separate case.