Rate of Change Quick Check

Front

What is the average rate of change?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Front

How do you calculate the average rate of change?

Back

Average Rate of Change = (f(b) - f(a)) / (b - a), where [a, b] is the interval.

Front

What does a positive average rate of change indicate?

Back

A positive average rate of change indicates that the function is increasing over the interval.

Front

What does a negative average rate of change indicate?

Back

A negative average rate of change indicates that the function is decreasing over the interval.

Front

If a climber's altitude changes from 600 feet to 1000 feet over 4 hours, what is the average rate of change?

Back

100 feet per hour.

Front

What is the significance of a constant rate of change?

Back

A constant rate of change means that the function increases or decreases at the same rate over the entire interval.

Front

How do you interpret a rate of change of 2 feet per second?

Back

It means that for every second that passes, the quantity (e.g., depth) changes by 2 feet.

Front

What is the average rate of change for a function that goes from 5 to 15 over an interval of 2 units?

Back

5 units per unit interval.

Front

What is the average rate of change if a diver goes from 50 feet below to 140 feet below in 45 seconds?

Back

The diver is descending at a rate of 2 feet per second.

Front

What does it mean if one company has a greater rate of change than another?

Back

It means that the first company is increasing or decreasing its output or performance at a faster rate.