Description
Classify a supplied stationary point by its second derivative.
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.
Classify a supplied stationary point by its second derivative.
When to use this tool
Use Calculus: Stationary Point Second Derivative Sign when checking the stated derivative-test or local stationary-point convention.
How to use the tool and how it works
- Enter secondDerivative, stationaryEstablished. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Classify a supplied stationary point by its second derivative. Require stationaryEstablished true; positive gives strict-local-minimum, negative strict-local-maximum, zero inconclusive.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| secondDerivative | Second Derivative | Required. Finite number. |
| stationaryEstablished | Required true assertion, not independent verification that the first derivative vanishes. | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Returned calculated value or nested object under the stated output convention. | Required. Object. |
| result.classification | Classification | Calculated result member: string. |
{
"input": {
"secondDerivative": 0,
"stationaryEstablished": true
},
"output": {
"result": {
"classification": "inconclusive"
}
}
}Limitations and assumptions
- Stationarity and differentiability assumptions must be established independently; a true flag does not verify them.
- Outputs are nested inside result. 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.
- Stationary Slope Curvature Ratio
Return a Newton offset for a stationary-slope equation.