1. ## second differentiation problem

Hello, I need to establish if:
t(tan(t)) is accelerating or deccelerating at t=pi/4

My attempt is:

1. differentiate to get velocity function:
tant + tsec^2t

2. differentiate again to find acceleration function
1/cos^2t + sec^2t + t(2sint/cos^3t)

3. Now I plug in pi/4 and get an acceleration of 7.142.

Hopefully I have the above all correct ?
Do I now simply use a pair of test points on either side of pi/4 to establish if the acceleration is increasing or decreasing ?
or does the fact that the acceleration is positive tell me that it is accelerating rather than deccelerating ?

Thanks for any help.

2. ## Re: second differentiation problem

Originally Posted by fran1942
Hello, I need to establish if:
t(tan(t)) is accelerating or deccelerating at t=pi/4

My attempt is:

1. differentiate to get velocity function:
tant + tsec^2t

2. differentiate again to find acceleration function
1/cos^2t + sec^2t + t(2sint/cos^3t)

3. Now I plug in pi/4 and get an acceleration of 7.142.

Hopefully I have the above all correct ?
Do I now simply use a pair of test points on either side of pi/4 to establish if the acceleration is increasing or decreasing ?
or does the fact that the acceleration is positive tell me that it is accelerating rather than deccelerating ?

Thanks for any help.
Looks to be correct. And it's the fact that the acceleration is positive that tells you the function is accelerating rather than decelerating.