Description
Compare supplied right and left derivative values.
Local calculus terms distinguish derivative components, signed interval widths, endpoint values and correction terms. A trapezoid correction is not the whole integral, and agreement of supplied derivatives does not prove differentiability. Scalar operations preserve the chosen direction and approximation rather than assessing the function globally.
Compare supplied right and left derivative values.
When to use this tool
Use One Sided Derivative Agreement Residual when you already have leftDerivative, rightDerivative and need to compare supplied right and left derivative values.
How to use the tool and how it works
- Enter leftDerivative, rightDerivative. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read signedGap. Use the output convention below.
Return rightDerivative-leftDerivative.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| leftDerivative | Left Derivative | Required. Finite number. |
| rightDerivative | Right Derivative | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| signedGap | rightDerivative-leftDerivative; agreeing supplied numbers do not prove differentiability. | Required. Finite number. |
{
"input": {
"leftDerivative": 12,
"rightDerivative": 17
},
"output": {
"signedGap": 5
}
}Limitations and assumptions
- Zero is exact scalar agreement only. No function, derivative existence, one-sided limit, differentiability, tolerance or smoothness is verified.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the full function, derivative or quadrature method for the mathematical problem. Check smoothness, interval orientation and approximation error separately; local supplied-value terms do not establish those conditions.
References
Similar or alternative tools
- Local Integral Rectangle Correction
Compare a supplied local integral with a left-rectangle term.
- Endpoint Trapezoid Correction Term
Calculate the trapezoid-minus-left-rectangle correction from supplied endpoints.