Basic Examples (1) 

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

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Scope (2) 

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

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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:

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Options (6) 

FontSize (1) 

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

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MinusColor (1) 

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

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PlusColor (1) 

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

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ZeroColor (1) 

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

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ShowEquations (1) 

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

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ShowPlots (1) 

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

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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:

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