Description
Locate the first derivative outside a supplied flatness tolerance.
Derivative tests classify local behavior only under their hypotheses, including a stationary point when required. An inconclusive or flat-within-tolerance result is distinct from a proved extremum; supplied derivatives and a chosen tolerance do not establish smoothness or a global optimum.
Locate the first derivative outside a supplied flatness tolerance.
When to use this tool
Use Scalar Critical Point Flatness Residual when checking the stated derivative-test or local stationary-point convention.
How to use the tool and how it works
- Enter derivatives, tolerance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read firstNonflatOrder, flatThrough. Use the output convention below.
Locate the first derivative outside a supplied flatness tolerance. Require nonempty derivatives and tolerance >= 0; firstNonflatOrder is the one-based first abs(value) > tolerance, or zero if none; flatThrough counts preceding tolerated derivatives.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| derivatives | Derivatives | Required. Array of finite number; maximum items 256. |
| tolerance | Nonnegative caller-selected comparison tolerance, in matching units. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| firstNonflatOrder | First derivative order outside tolerance, or zero sentinel when none is found. | Required. Safe integer. |
| flatThrough | Flat Through | Required. Safe integer. |
{
"input": {
"derivatives": [
0,
0,
6
],
"tolerance": 0
},
"output": {
"firstNonflatOrder": 3,
"flatThrough": 2
}
}Limitations and assumptions
- Zero order is a no-witness sentinel; numerical flatness is not proof of vanishing derivatives or an analytic critical-point classification.
- 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
Verify the actual function, stationarity and smoothness assumptions, then use the relevant complete local or global analysis to establish an extremum.
References
Similar or alternative tools
- Critical Point Second Derivative Discriminant
Apply the two-variable Hessian determinant test to supplied entries.
- Calculus: Stationary Point Second Derivative Sign
Classify a supplied stationary point by its second derivative.