# Derivatives

### Example 1

Peggy drove from New York to Boston (a distance of 219 miles) in 4 hours. What was her average rate of travel?

### Example 2

Lou was 20 miles from home at 1 pm and 120 miles from home at 3 pm. What was Lou's average rate of travel during that time?

### Example 3

The graph shows John's starting and ending distances from home on a recent trip. Calculate his average rate of travel during the trip.

### Example 4

The graph shows Suhaila's position during a trip. Calculate Suhaila's average rate of travel between 2 pm and 2:30 pm.

### Example 5

Roger likes to eat jellybeans. One day he ate 56 jellybeans in 7 minutes. On average, how many jellybeans did he eat per minute?

### Example 6

- When there are two mome raths in the forest, there are three borogoves. When there are twenty mome raths in the forest, there are 15 borogoves. What is the average rate of change of borogoves with respect to mome raths?

### Example 7

An army is using catapults against their enemy. They go through the catapults one at a time, tossing them aside when they break. After the first catapult breaks they've thrown 20 stones. After the 19th catapultbreaks, they've thrown 220 stones. On average, how many stones does each catapult throw?

### Example 8

Alice went to Wonderland and visited a succession of tea parties given by the Mad Hatter. The number of dormice at the tea parties changed depending on the number of teapots laid out. A party with 3 teapots would have only one dormouse, but a party with 14 teapots would have 24 dormice. What was the average rate of change of dormice with respect to teapots?