Exploring Average Rate of Change in Calculus

What is the main focus of the first lesson in the new unit?

• Introduction to average rate of change

• Introduction to derivatives

• Introduction to integrals

• Introduction to limits

What is another term for the average rate of change?

• Limit

• Slope

• Integral

• Derivative

In the context of average rate of change, what does Delta Y/Delta X represent?

• The change in Y over the change in X

• The change in X over the change in Y

• The sum of X and Y

• The product of X and Y

What is the secant line?

• A line that touches the curve at one point

• A line that intersects the curve at two points

• A line that is parallel to the curve

• A line that is perpendicular to the curve

In the first example, what is the function used to find the average rate of change?

• 3x^2 - 2x

• x^3 - 2x

• 2x^2 - 3x

• x^2 - 3x

What is the average rate of change between 1/2 and 3/2 for the function x^3 - 2x?

• 0.5

• 1.25

• 1.75

• 0.625

In the second example, what is the dependent variable?

• Time

• Distance

• Number of kids

• Hours

How many hours per kid does it take Mr. Bress to clean his house on average?

• 12 hours

• 18 hours

• 14 hours

• 16 hours

What does the interval X to X + h represent in the context of average rate of change?

• A decreasing interval

• A constant interval

• A variable interval

• A specific numerical interval

Why is understanding the average rate of change with variables important?

• It helps in understanding integrals

• It helps in understanding limits

• It helps in understanding the definition of the derivative

• It helps in understanding the concept of continuity