# Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

Compute properties of the tangent and normal lines to a curve at a given point

Contributed by:
Wolfram|Alpha Math Team

ResourceFunction["TangentAndNormalLine"][ gives an association of properties of the tangent and normal lines to | |

ResourceFunction["TangentAndNormalLine"][ returns the value of the tangent and normal lines property | |

ResourceFunction["TangentAndNormalLine"][ returns information relating to one pair, among possibly several, of the tangent and normal lines to | |

ResourceFunction["TangentAndNormalLine"][ returns information relating to one pair, among possibly several, of the tangent and normal lines to |

Allowed values of *prop* are:

"SlopeInterceptEquation" | equation of the tangent line in slope intercept form |

"StandardFormEquation" | equation of the tangent line in standard form |

"PointSlopeEquation" | equation of the tangent line in point slope form |

"HorizontalIntercept" | horizontal intercept for the tangent line equation |

"VerticalIntercept" | vertical intercept for the tangent line equation |

"Plot" | plot of the tangent line equation |

All | association of information returning all allowed properties |

If *expr* does not have head Equal, then *expr* is treated as an expression defining *y* in terms of *x*. In other words, ResourceFunction["TangentAndNormalLine"][*expr*,{*x*,*a*},*y*,…] is equivalent to ResourceFunction["TangentAndNormalLine"][*y*==*expr*,{*x*,*a*},*y*,…] if *expr* has a head other than Equal.

If only one coordinate of the intersection point is given, the other coordinate is inferred. For expressions that are multivalued at the given value of *x* or *y*, information on only one of potentially several tangent and normal line pairs is returned.

Compute the slope-intercept equations of the tangent and normal lines to a curve at a given point:

In[1]:= |

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Visualize this result:

In[2]:= |

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Compute the slope of these tangent and normal lines:

In[3]:= |

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Compute the horizontal intercepts of these tangent and normal lines:

In[4]:= |

Out[4]= |

Get the standard-form equation of these tangent and normal lines:

In[5]:= |

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Get an association of properties of the tangent and normal lines to a curve:

In[6]:= |

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Get just the point-slope equations:

In[7]:= |

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The first argument to TangentAndNormalLine can be an implicit definition of a curve:

In[8]:= |

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If a tangent or normal line is parallel to a coordinate axis, its intercept with that axis is None:

In[9]:= |

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If a position for *y* is not specified, information on only one of the possible normal lines at the given *x* value is returned:

In[10]:= |

Out[10]= |

Requesting tangent and normal lines information about a point that is not on the curve will result in an error message:

In[11]:= |

Out[11]= |

Vertical tangent lines (whose slope cannot be computed) are plotted as dotted lines. Some of their properties may not be defined:

In[12]:= |

Out[12]= |

If a function has a cusp or a discontinuity at the given point, no tangent or normal line is returned:

In[13]:= |

Out[13]= |

- Normal Line–Wolfram MathWorld
- Tangent Line–Wolfram MathWorld
- Explore a Golden rectangle with TangentAndNormalLine in WFR"–Wolfram Community

- 2.0.0 – 23 March 2023
- 1.0.0 – 15 June 2021

This work is licensed under a Creative Commons Attribution 4.0 International License