3.3 Rates of Change

• What is the formula for speed in terms of distance and time?

  Distance / Time
• Steps to calculate average rate of change from a table

  1️⃣ Identify the change in quantity over a given time interval

  2️⃣ Divide the change in quantity by the change in time
• What is the formula for average rate of change?

  (Change in Quantity) / (Change in Time)
• When calculating the average rate of change from a graph, you divide the change in quantity by the change in time.


  True
• When working with tables, you must identify the change in quantity over a given time interval to calculate the average rate of change.


  True
• The instantaneous rate of change is calculated using the slope of the tangent.


  True
• The average rate of change is calculated over an interval, while the instantaneous rate is calculated at a single point.

  True
• Understanding the rate of change can help predict investment performance in finance.

  True
• What does the rate of change measure?

  How one quantity changes
• What is the formula for average rate of change?

  (Change in Quantity) / (Change in Time)
• The instantaneous rate of change at a specific point is the slope of the tangent
• If a plant grows 10 cm in 5 days, the average rate of growth is 2 cm/day.
• What is the formula for average rate of change?

  (Change in Quantity) / (Change in Time)
• What is the average rate of change for a car that travels 100 meters in 5 seconds?

  20 m/s
• What mathematical tool is used to find the instantaneous rate of change?

  Derivatives
• In engineering, the rate of change is used to analyze flow rates of fluids.
• Speed is the change in distance over time
• If a plant grows 10 cm in 5 days, its average rate of growth is 2 cm/day
• What does the speedometer of a car measure at any given second?

  Instantaneous speed
• How do you find the average rate of change from a table?

  Change in quantity / Change in time
• Match the type of rate of change with its definition:

  Average Rate of Change ↔️ Change over a finite time interval

  Instantaneous Rate of Change ↔️ Change at a specific point
• Steps to find the instantaneous rate of change using derivatives:

  1️⃣ Find the derivative of the function

  2️⃣ Evaluate the derivative at the specific point in time
• The average rate of change measures the average change in a quantity over a specified interval
• The average rate of change considers the change at a single point.

  False
• The average rate of change is found by dividing the total change in the quantity by the time taken.


  True
• If a plant grows 10 cm in 5 days, the average rate of growth is 2 cm/day.
• Suppose a car's distance traveled is recorded in a table. The average rate of change is calculated using the change in distance and time.
• The instantaneous speed of a car is what the speedometer shows at any given second.
• In which field is the rate of change used to describe velocity?

  Physics