Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 DerivativeSignCharts

Source Notebook

Get a grid of sign charts for a function and its first and second derivatives

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["DerivativeSignCharts"][f, x]

creates a grid of sign charts for f(x),f'(x) and f''(x).

Details

DerivativeSignChart accepts all of the options of NumberLinePlot, as well as the following options:
FontSizeMediumadjust the font size of sign chart labels
"PlusColor"set the color corresponding to positive points/intervals
"MinusColor"set the color corresponding to negative points/intervals
"ZeroColor"set the color corresponding to zero or discontinuous points/intervals
"ShowPlots"Falseinclude plots of the function and its derivatives in the grid
"ShowEquations"Falseinclude equations of the function and its derivatives in the grid

Examples

Basic Examples (1) 

Get sign charts for x3 and its first and second derivatives (3x2 and 6x, respectively):

In[1]:=
ResourceFunction["DerivativeSignCharts"][x^3, x]
Out[1]=

Scope (2) 

Include the equations and plots of the given function and its derivatives:

In[2]:=
ResourceFunction["DerivativeSignCharts"][x^3 - 8 x + 7, x, "ShowPlots" -> True, "ShowEquations" -> True]
Out[2]=

If there are infinitely many places where a function or one of its derivatives changes signs, the sign chart displays information for an interval surrounding x = 0:

In[3]:=
ResourceFunction["DerivativeSignCharts"][Tan[x], x, "ShowEquations" -> True]
Out[3]=

Options (6) 

FontSize (1) 

Use the option FontSize to adjust the size of the sign chart labels:

In[4]:=
ResourceFunction["DerivativeSignCharts"][x^3 - 8 x + 7, x, FontSize -> 18]
Out[4]=

MinusColor (1) 

Use the option "MinusColor" to adjust the color of the negative intervals and minus signs:

In[5]:=
ResourceFunction["DerivativeSignCharts"][x^3 - 8 x + 7, x, "MinusColor" -> Red]
Out[5]=

PlusColor (1) 

Use the option "PlusColor" to adjust the color of the positive intervals and plus signs:

In[6]:=
ResourceFunction["DerivativeSignCharts"][x^3 - 8 x + 7, x, "PlusColor" -> Red]
Out[6]=

ZeroColor (1) 

Use the option "ZeroColor" to adjust the color of the zero or discontinuous intervals and zeros:

In[7]:=
ResourceFunction["DerivativeSignCharts"][x^3 - 8 x + 7, x, "ZeroColor" -> Red]
Out[7]=

ShowEquations (1) 

Set option “ShowEquations” to True to show the equations of the inputted function and its derivatives:

In[8]:=
ResourceFunction["DerivativeSignCharts"][x^3 - 8 x + 7, x, "ShowEquations" -> True]
Out[8]=

ShowPlots (1) 

Set option “ShowPlots” to True to show plots of the inputted function and its derivatives:

In[9]:=
ResourceFunction["DerivativeSignCharts"][(x + 3)/(x - 2), x, "ShowPlots" -> True]
Out[9]=

Applications (1) 

Sign charts are a useful reasoning tool in many contexts, especially calculus and functional analysis. Comparing the behavior of a function to the signs of its derivatives is foundational to the first and second derivative tests:

In[10]:=
ResourceFunction["DerivativeSignCharts"][x^3 - 6 x, x, "ShowPlots" -> True]
Out[10]=

Publisher

Wolfram|Alpha Math Team

Version History

  • 2.0.0 – 23 March 2023
  • 1.0.0 – 14 October 2022

Related Resources

Author Notes

To view the full source code for DerivativeSignCharts, evaluate the following:

License Information