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.
- 3 variables
- 2 worked examples
- 15 in Applications of Derivatives
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
- 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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Common questions
What is the Normal Line?
The normal line is perpendicular to the tangent line. Its slope is the negative reciprocal of the derivative. It is one of the applications of derivatives formulas in the CalcRef reference.
When does the Normal Line apply?
The Normal Line holds under this condition: f'(a) ≠ 0.
How do you use the Normal Line?
Worked example. 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.
Practice
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