Week 4 - Average Rate of Change

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 f(b) and f(a) are the function values at points b and a.

Front

If a climber is at 400 feet after 2 hours and 700 feet after 6 hours, what is the average rate of change?

Back

Average Rate of Change = (700 - 400) / (6 - 2) = 75 feet per hour.

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

What is the average rate of change from x=1 to x=5 if f(1) = 2 and f(5) = -2?

Back

Average Rate of Change = (-2 - 2) / (5 - 1) = -1.

Front

What is the average rate of change of a rocket's altitude from 1.5 miles to 8 miles in 2 minutes?

Back

Convert 2 minutes to seconds: 2 minutes = 120 seconds. Average Rate of Change = (8 - 1.5) / 120 = 0.0554 miles per second.

Front

What is the significance of the average rate of change in real-world applications?

Back

It helps to understand how a quantity changes over time, such as speed, growth rates, and trends.

Front

If a function is linear, how does the average rate of change behave?

Back

For a linear function, the average rate of change is constant over any interval.

Front

What is the average rate of change if a function increases from 3 to 15 over an interval of 4 units?

Back

Average Rate of Change = (15 - 3) / (b - a) = 3 units per unit interval.

Front

How can you interpret the average rate of change graphically?

Back

It is represented by the slope of the secant line connecting two points on the graph of the function.