Applications of Derivatives · Tangent & Normal Lines
Tangent Line
The equation of the tangent line to f(x) at the point (a, f(a)). The slope is the derivative evaluated at x = a.
Variables
| Symbol | Name | Unit |
|---|---|---|
| a | x-coordinate The x-value of the point of tangency | — |
| fa | f(a) The y-value at x = a | — |
| fpa | f'(a) The derivative (slope) at x = a | — |
Worked examples
Find the tangent line to f(x) = x² at x = 3.
- f(3) = 9, f'(x) = 2x, f'(3) = 6
- y - 9 = 6(x - 3)
- y = 6x - 9
Answer: y = 6x - 9
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