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.
- 3 variables
- 2 worked examples
- 15 in Applications of Derivatives
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
- 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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Common questions
What is the 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. It is one of the applications of derivatives formulas in the CalcRef reference.
What do the symbols in the Tangent Line mean?
In the Tangent Line, a is the x-coordinate; fa is the f(a); fpa is the f'(a).
How do you use the Tangent Line?
Worked example. 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.
Practice
Quiz yourself on Applications of Derivatives
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