Download your Word document
Cubic Critical Points result sheet — free, supported by sponsors. Your download button appears in 20 seconds.
This free download is supported by sponsors — continuing in
20
Your file is generated in your browser when you choose Download — nothing is uploaded. If this calculator returns enough numeric data, the export also includes its best-fit chart alongside the readable table.
WorldCalculate result export
Cubic Critical Points — result sheet
Stationary x-values where the derivative of a cubic is zero.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: f' = 3a x^2 + 2b x + c; D = (2b)^2 - 12ac; x = (-2b +/- sqrt(D))/6a.
Differentiate term by term, then solve the quadratic derivative. A negative discriminant means monotone cubic with no real stationary point.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- a (x^3) — Must not be zero.; minimum -1000000000; maximum 1000000000
- b (x^2) — minimum -1000000000; maximum 1000000000
- c (x) — minimum -1000000000; maximum 1000000000
- d (constant) — Shifts f; does not move critical points.; minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| a (x^3) | 1 |
| b (x^2) | -3 |
| c (x) | 0 |
| d (constant) | 5 |
Critical points x = 0 and x = 2.
Assumptions and limits
- Genuine cubic: leading coefficient ca is nonzero.
- Real coefficients; critical points solve f-prime equals zero.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
No saved result was found. Please run the calculation first, then choose Download again.