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Instantaneous and Average Velocity

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Consider the following statements regarding the position function s(t)=t2+2t+1s(t) = t^2 + 2t + 1.

I. The instantaneous velocity is given by the derivative, s′(t)=2t+2s'(t) = 2t + 2.
II. At time t=3t=3, the instantaneous velocity is s′(3)=2(3)+2=8s'(3) = 2(3) + 2 = 8.
III. The average velocity on the interval [3,4][3, 4] is equal to the instantaneous velocity at t=3.5t=3.5.

Which of the statements above is/are true?

A

Only I. and II. are true.

B

Only II. and III. are true.

C

I., II., and III. are true.

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