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t S(t)
0 0
2 60
4 160
6 310
8 400

The differentiable function $S$ represents the distance traveled by a vehicle over an $8\text{ hour}$ period. Distance is measured in miles and $t =\text{number of hours}$. The table above shows $S(t)$ every $2\text{ hours}$.

In what interval must there be a time when $S^{ \prime }\left( t \right) =60\text{ miles per hour}$?

A

$0 < t < 2$

B

$0 < t < 4$

C

$2 < t < 6$

D

$4 < t < 8$

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