# Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

Compute properties of the tangent line to a curve at a given point

Contributed by:
Wolfram|Alpha Math Team

ResourceFunction["TangentLine"][ returns an association of properties of the tangent line to | |

ResourceFunction["TangentLine"][ returns the value of the tangent line property | |

ResourceFunction["TangentLine"][ returns information relating to one, among possibly several, of the tangent lines to | |

ResourceFunction["TangentLine"][ returns information relating to one, among possibly several, of the tangent 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 |

"Slope" | slope of the tangent line |

"PointOfTangency" | point at which tangent line is computed |

"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["TangentLine"][*expr*,{*x*,*a*},*y*,…] is equivalent to ResourceFunction["TangentLine"][*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 lines is returned.

Compute the slope-intercept equation of the tangent line to a curve at a given point:

In[1]:= |

Out[1]= |

Visualize this result:

In[2]:= |

Out[2]= |

Compute the slope of this tangent line:

In[3]:= |

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Compute the horizontal intercept of this tangent line:

In[4]:= |

Out[4]= |

Get the standard-form equation of this tangent line:

In[5]:= |

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Get an Association of properties of a tangent line to a curve:

In[6]:= |

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Get just the point-slope equation of this tangent line:

In[7]:= |

Out[7]= |

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

In[8]:= |

Out[8]= |

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

In[9]:= |

Out[9]= |

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

In[10]:= |

Out[10]= |

If one coordinate is not specified, information on only one of the possible tangent lines at the given coordinate value is returned:

In[11]:= |

Out[11]= |

Vertical tangent lines have infinite slope. 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 line is returned:

In[13]:= |

Out[13]= |

- 5.1.0 – 04 August 2023
- 5.0.0 – 23 March 2023
- 4.0.1 – 28 March 2022
- 4.0.0 – 26 May 2021
- 3.0.0 – 24 January 2020
- 2.0.0 – 06 September 2019
- 1.0.0 – 23 August 2019

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