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.