Applications of Derivatives · Tangent & Normal Lines
Normal Line
The normal line is perpendicular to the tangent line. Its slope is the negative reciprocal of the derivative.
Conditions. f'(a) ≠ 0.
Variables
| Symbol | Name | Unit |
|---|---|---|
| a | x-coordinate The x-value of the point | — |
| fa | f(a) The y-value at x = a | — |
| fpa | f'(a) The derivative at x = a | — |
Worked examples
Find the normal line to f(x) = x² at x = 3.
- f(3) = 9, f'(3) = 6
- Normal slope = -1/6
- y - 9 = (-1/6)(x - 3)
Answer: y = -x/6 + 19/2
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