Calculus
posted by Janet .
The position in meters of a particle is given by f(t)= 14t3t^2, where t is measured in seconds.
a) Evaluate f'(2) and interpret the results.
This is how I solved this. f'(t)=146t= 2(73t)
f'(2)=2(73(2))= 2 This means the velocity of the particle is 2 m/s when t=2.
b) On what intervals is the particle speeding up?
I don't know how to do this part.
Please help

f'=146t
correct on a)
b)
f'>0
146t>0
or t<14/6 so it is speeding up for all t less than 14/6