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Derivative at a Point (Central Difference) — result sheet
Estimates f'(a) from two nearby function values using the symmetric central-difference quotient.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: f'(a) ≈ (f(a+h) − f(a−h)) / (2h).
The symmetric quotient cancels first-order error, so it beats one-sided differences on smooth functions. It needs only the two values, not the formula for f.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- f(a − h) — Function value just below a.; minimum -1000000000000; maximum 1000000000000
- f(a + h) — Function value just above a.; minimum -1000000000000; maximum 1000000000000
- Step size h — Small positive spacing; h = 0 is invalid.; minimum 1.0E-9; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| f(a − h) | 7.2 |
| f(a + h) | 8.8 |
| Step size h | 0.2 |
Estimated derivative 4.
Assumptions and limits
- f is smooth near a; noisy or kinked data degrades the estimate.
- h is small and positive; h = 0 is undefined.
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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