Exploring Average Rate of Change in Functions

This video tutorial explains how to compute the average rate of change of a function. It begins with the definition and formula, emphasizing the importance of maintaining the correct order of terms. The video then provides two examples: calculating the average rate of change from x=1 to x=2 and from x=-1 to x=6, demonstrating the step-by-step process and highlighting the significance of order in calculations.

What is the formula for calculating the average rate of change of a function?

• F of B minus F of A divided by B minus A

• F of A minus F of B divided by A minus B

• F of A minus F of B divided by B minus A

• F of B minus F of A divided by A minus B

When calculating the average rate of change, why is it important to maintain the order of points?

• To ensure the result is positive

• To avoid incorrect calculations

• To simplify the formula

• To make the calculation faster

What should you do if you switch the order of points in the average rate of change formula?

• Switch the order on the bottom as well

• Subtract the points from each other

• Nothing, the result will be the same

• Add the points together

In the example calculation from x=1 to x=2, what is F of 1?

• 3

• 4

• 1

• 2

In the example calculation from x=1 to x=2, what is F of 2?

• 5

• 2

• 3

• 4

What is the average rate of change from x=1 to x=2 for the function f(x) = 4x - x^2?

• 0

• 1

• 2

• 3

In the example calculation from x=-1 to x=6, what is F of -1?

• 2

• 5

• 3

• 4

In the example calculation from x=-1 to x=6, what is F of 6?

• -10

• -11

• -12

• -13

What is the average rate of change from x=-1 to x=6 for the function f(x) = 4x - x^2?

• 0

• 1

• -1

• -2

What is the result of 6 - (-1) in the context of the average rate of change calculation?

• 7

• 6

• 8

• 5