So I have been thinking of this problem... what is the greatest rate of angle change for a function? As in, what is the point in which a function achieves its greatest rate of angle change....(adsbygoogle = window.adsbygoogle || []).push({});

Well, the angle of a function can be determined by arctan(y')

The Rate of Angle change is (arctan(y'))', which equals [itex]\frac{y'}{(y')^2 +1}[/itex]

So the greatest rate of angle change is the derivative of that set to zero, which is equal to

[itex]\frac{y''' - 2(y')^2y' + y'''(y')^2}{((y')^2 +1)} = 0[/itex]

Which , you can simplify to....

[itex]y''' - 2(y')^2y' + y'''(y')^2= 0[/itex]

Is there a way that this differential equation can be solved? (This is not for homework, this is just a general question that I would like to know the answer to)

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Greatest Rate of Angle Change

Loading...

Similar Threads - Greatest Rate Angle | Date |
---|---|

I Rate of change of area under curve f(x) = f(x) | Jan 2, 2018 |

Definite integral of greatest integer function | Mar 17, 2015 |

One Sided Limits of Greatest Integer Function | Sep 10, 2012 |

Limit of the greatest integer number | Jan 27, 2012 |

Finding limit- greatest integer function | Nov 14, 2011 |

**Physics Forums - The Fusion of Science and Community**