Description
Compare a secant slope with a supplied derivative.
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 a secant slope with a supplied derivative.
When to use this tool
Use Secant Derivative Discrepancy when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter x0, x1, y0, y1, suppliedDerivative. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read secant, discrepancy. Use the output convention below.
Compare a secant slope with a supplied derivative. Require x0 != x1; secant = (y1-y0)/(x1-x0), discrepancy = secant-suppliedDerivative.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x0 | X0 | Required. Finite number. |
| x1 | X1 | Required. Finite number. |
| y0 | Y0 | Required. Finite number. |
| y1 | Y1 | Required. Finite number. |
| suppliedDerivative | Supplied Derivative | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| secant | Secant | Required. Finite number. |
| discrepancy | Discrepancy | Required. Finite number. |
{
"input": {
"x0": 1,
"x1": 3,
"y0": 1,
"y1": 9,
"suppliedDerivative": 2
},
"output": {
"secant": 4,
"discrepancy": 2
}
}Limitations and assumptions
- No underlying function, limiting derivative or statistical measurement tolerance is evaluated.
- 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 Line From Point Derivative
Evaluate a supplied tangent-line approximation.
- Tangent Axis Intercept
Return axis intercepts of a supplied nonhorizontal tangent line.