Polynomial Calculator
Last updated: November 5, 2026
Evaluate a cubic polynomial and its first two derivatives at a selected x value.
Polynomial value
—
- First derivative at x: —
- Second derivative at x: —
- Polynomial expression: —
On this page
Quick summary: Evaluate a cubic polynomial and its first two derivatives at a selected x value.
Read the complete guide
Updated reference sections in this guide are in English.
What this calculator estimates
Evaluate a cubic polynomial and its first two derivatives at a selected x value.
How to use it
Enter x³ coefficient a; x² coefficient b; x coefficient c; Constant d; x value. Select Calculate to update the results.
How the calculation works
Horner’s method evaluates the cubic efficiently. The derivative formulas are 3ax² + 2bx + c and 6ax + 2b.
Worked example: starting scenario
| x³ coefficient a | 1 |
|---|---|
| x² coefficient b | -2 |
| x coefficient c | 3 |
| Constant d | -4 |
| x value | 2 |
| Polynomial value | 2 |
|---|---|
| First derivative at x | 7 |
| Second derivative at x | 8 |
| Polynomial expression | 1x³ + -2x² + 3x + -4 |
Important limitations
This page evaluates a polynomial; it does not find all polynomial roots.
Value, slope and curvature are different outputs
For f(x) = 2x³ − 3x² + 4x + 5, the first derivative is 6x² − 6x + 4 and the second derivative is 12x − 6. At x = 2, these give f(2) = 17, slope 16 and second derivative 18. The calculator evaluates a cubic and its derivatives at one x; it does not find every root or an interval of increasing values.