Calculus

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The position in meters of a particle is given by f(t)= 14t-3t^2, where t is measured in seconds.

a) Evaluate f'(2) and interpret the results.

This is how I solved this. f'(t)=14-6t= 2(7-3t)

f'(2)=2(7-3(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.

• Calculus -

f'=14-6t

correct on a)

b)
f'>0
14-6t>0
or t<14/6 so it is speeding up for all t less than 14/6

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