Description
Evaluate a supplied tangent-line approximation.
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.
Evaluate a supplied tangent-line approximation.
When to use this tool
Use Calculus: Tangent Line From Point Derivative when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter x, anchorX, anchorY, derivative. 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.
Evaluate a supplied tangent-line approximation. linearizedY = anchorY+derivative*(x-anchorX).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | X | Required. Finite number. |
| anchorX | Anchor X | Required. Finite number. |
| anchorY | Anchor Y | Required. Finite number. |
| derivative | Derivative | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Returned calculated value or nested object under the stated output convention. | Required. Object. |
| result.linearizedY | Linearized Y | Calculated result member: number. |
{
"input": {
"x": 3,
"anchorX": 1,
"anchorY": 4,
"derivative": 2
},
"output": {
"result": {
"linearizedY": 8
}
}
}Limitations and assumptions
- Derivative and anchor are supplied; no function is differentiated and no approximation-error bound is established.
- 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
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.
- Tangent Axis Intercept
Return axis intercepts of a supplied nonhorizontal tangent line.