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 $S^{ \prime }\left( t \right) =60\text{ miles per hour}$?

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