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.