Maths Polynomial Root Maximum And Minimum And Point Of Inflection

Calculate maths polynomial roots, maximum and minimum and points of inflection.

Multiple roots, maximum and minimum or points of inflection are calculated using the Durand Kerner method. This method is only valid if all roots, maximum and minimum or points of inflection are real. Use the single root calculators for polynomials with imaginary roots. The single root calculators can only calculate real roots, maximum and minimum or points of inflection. The value Xu is used as the initial guess for calculating the roots, maximum and minimum or points of inflection. Use the plot options to select suitable guess values.

Change Module :

Maths Polynomial Calculation Module
Maths Polynomial Coefficient Calculation Module
Maths Polynomial Interpolation Calculation Module
All

[FREE] tools are free in basic mode with no login (no plots, tables, goal seek etc). Login or Open a free account to use the tools in plus mode (with plots, tables, goal seek etc).
[PLUS] tools are free in basic CHECK mode with Login or Open a free account (CHECK values no plots, tables, goal seek etc). Buy a Subscription to use the tools in plus mode (with plots, tables, goal seek etc).
Try plus mode using the Plus Mode Demo tools with no login. Help Using The Pipeng Toolbox (opens in the popup workbook)

Links : ±

CALCULATOR : Polynomial Single Real Root Or Zero [FREE] ±

Calculate polynomial real root or zero, maximum or minimum (zero slope), or point of inflection (zero curvature).

The polynomial value, slope and curvature are calculated at either the user defined X, the root or zero, the maximum or minimum, or the point of inflection. The maximum and minimum can only be calculated for polynomials of second order or greater. The point of inflection can only be calculated for polynomials of third order or greater. The root, maximum or minimum, or point of inflection must be real.

The user defined Xu value is used as the initial guess value for calculating the root and other points. Use the Result Plot option to plot the polymomial value, slope and curvature versus X, and to determine suitable guess values for Xu.

Tool Input

ptype : Polynomial Calculation Type
- Xu : User Defined X Value or Guess Value
A : Polynomial Coefficients

Tool Output

C : Polynomial Curvature At X
P : Polynomial Value At X
S : Polynomial Slope At X
X : X Value (Input, Root, Maximum or Minimum, Or Inflection Point)
cvg : Convergence (== 1)

CALCULATOR : Polynomial All Real Roots Or Zeros [FREE] ±

Calculate all polynomial real roots or zeros, maximum and minimum (zero slope), and points of inflection (zero curvature).

Enter the polynomial coefficients as a comma separated list, or as separate points on each line. The coefficients can also be copied and pasted from a spreadsheet. The coefficients must be in order A0, A1, A2....An where An is the coefficient for the nth power of x (x^n) etc... The root or zero calculation will cause an error if any of the roots are imaginary, or in some cases with multiple equal roots. Use the single root calculator if there is an error. Imaginary maximum and minimum points, or points of inflection will also cause an error. Use the Result Plot option to plot the polynomial value, slope and curvature.

Tool Input

A : Polynomial Coefficients
X : Input X Value

Tool Output

C : Polynomial Curvature At X
P : Polynomial Value At X
S : Polynomial Slope At X

CALCULATOR : Quadratic Polynomial [FREE] ±

Calculate quadratic polynomial value, slope, curvature, real roots or zeros, and maximum or minimum (zero slope).

Quadratic second order polynomials have three coefficients. The coefficients must be in order A0, A1, A2 where A2 is the coefficient for the 2nd power of x (x^2) etc... Enter the polynomial coefficients as a comma separated list, or as separate points on each line. The coefficients can also be copied and pasted from a spreadsheet. Quadratics have constant curvature with a single maximum or minimum, and no point of inflection. Use the Result Plot option to plot the polynomial value, slope and curvature.

Tool Input

A : Polynomial Coefficients
X : Input X Value

Tool Output

C : Polynomial Curvature At X
P : Polynomial Value At X
S : Polynomial Slope At X