# Derivatives

### Example 1

According to Google Maps, it's 241 miles from Ann Arbor to Chicago. If Kevin made this trip in 4 hours, what was his average rate of travel during the trip? |

### Example 2

Liana was 10 miles from home at 2 pm and 70 miles from home at 3:15 pm. What was her average rate of travel during the trip? |

### Example 3

A famous author signed 200 books in two and a half hours. Find the average rate of change of the number of books signed with respect to the number of hours elapsed. |

### Example 4

Thomas went mountain climbing and took some trail mix. After climbing 200 feet he had eaten three handfuls of trail mix. On average, how many handfuls of trail mix did he consume per foot? |

### Example 5

Veronica has a tendency to forget about her cookies and leave them in the oven until the smoke alarm goes off. If she bakes her cookies at 300°F, it takes three-quarters of an hour for the smoke alarm to go off. If she bakes her cookies at 450°F (for those friends who like them...crispy), it only takes 10 minutes for the smoke alarm to go off. What is the average rate of change of time until the smoke alarm goes off with respect to oven temperature (in degrees Fahrenheit)? |