- #1
Gackhammer
- 13
- 0
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...
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)
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)