Description
Return axis intercepts of a supplied nonhorizontal tangent line.
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.
Return axis intercepts of a supplied nonhorizontal tangent line.
When to use this tool
Use Tangent Axis Intercept when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter x, y, derivative. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read xIntercept, yIntercept. Use the output convention below.
Return axis intercepts of a supplied nonhorizontal tangent line. Require derivative != 0; xIntercept = x-y/derivative, yIntercept = y-derivative*x.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | X | Required. Finite number. |
| y | Y | Required. Finite number. |
| derivative | Derivative | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| xIntercept | X Intercept | Required. Finite number. |
| yIntercept | Y Intercept | Required. Finite number. |
{
"input": {
"x": 2,
"y": 4,
"derivative": 4
},
"output": {
"xIntercept": 1,
"yIntercept": -4
}
}Limitations and assumptions
- The source curve and derivative are not verified; zero slope is rejected even though its y-intercept alone would exist.
- 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.
- Calculus: Tangent Normal Slope Orthogonality
Compare finite tangent and normal slopes for orthogonality.