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Tangent Line Equation — result sheet
Builds the tangent line at x = a from the function value and derivative.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: y = f(a) + f'(a)(x − a).
Point-slope form through (a, f(a)) with slope f'(a). It is also the first-order Taylor approximation near a.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- f(a) — Function value at a.; minimum -1000000000000; maximum 1000000000000
- Derivative f'(a) — Slope at a.; minimum -1000000000000; maximum 1000000000000
- Point a — minimum -1000000000000; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| f(a) | 3 |
| Derivative f'(a) | 2 |
| Point a | 1 |
y = 3 + 2(x - 1); slope 2 at (1, 3).
Assumptions and limits
- f is differentiable at a so a single slope exists.
- Approximation is local; accuracy fades far from a.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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