Description
Compare supplied left and right slopes.
Differential-calculus formulas relate supplied local values and derivatives under explicit coordinate and unit conventions. A tangent term, curvature expression or directional derivative assumes the required differentiability and regularity; substituting numerical derivatives does not verify those hypotheses for an actual function.
Compare supplied left and right slopes.
When to use this tool
Use One Sided Slope Disagreement when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter leftSlope, rightSlope, tolerance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read gap, agreesWithinTolerance. Inspect agreesWithinTolerance before interpreting the associated values.
Compare supplied left and right slopes. Require tolerance >= 0; gap = rightSlope-leftSlope, agreesWithinTolerance uses abs(gap) <= tolerance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| leftSlope | Left Slope | Required. Finite number. |
| rightSlope | Right Slope | Required. Finite number. |
| tolerance | Nonnegative caller-selected comparison tolerance, in matching units. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| gap | Signed difference under the stated comparison convention, with matching units. | Required. Finite number. |
| agreesWithinTolerance | Agrees Within Tolerance | Required. Boolean. |
{
"input": {
"leftSlope": 2,
"rightSlope": 3,
"tolerance": 0.5
},
"output": {
"gap": 1,
"agreesWithinTolerance": false
}
}Limitations and assumptions
- Agreement of supplied slopes does not verify existence of one-sided derivatives or differentiability of a real function.
- 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
Differentiate or validate the complete function and its domain first; use suitable symbolic or numerical methods and check regularity and coordinate conventions for the intended interpretation.
References
Similar or alternative tools
- Calculus: Tangent Normal Slope Orthogonality
Compare finite tangent and normal slopes for orthogonality.
- Secant Derivative Discrepancy
Compare a secant slope with a supplied derivative.