Understanding Average Rate of Change

The video tutorial explores how to calculate the average rate of change for a given function, y = 1/8 x^3 - x^2, over different intervals. The instructor demonstrates the process by evaluating the function at specific points and calculating the change in y over the change in x. The first interval, from -2 to 2, results in an average rate of change of 1/2, which matches the target rate. The second interval, from 0 to 4, is analyzed to show a different rate of change, confirming the correct interval was initially chosen.

What is the function given in the problem?

• y = x^3 - 1/8 x^2

• y = 1/8 x^2 - x^3

• y = x^2 - 1/8 x^3

• y = 1/8 x^3 - x^2

What is the value of y when x is -2?

• -3

• 2

• -5

• 0

What is the average rate of change of y with respect to x over the interval -2 to 2?

• -1/2

• 2

• 1/2

• 1

How much does y change when x changes from -2 to 2?

• -2

• -4

• 4

• 2

What is the value of y when x is 4?

• -8

• 0

• -4

• 8

What is the average rate of change of y with respect to x over the interval 0 to 4?

• -2

• 1/2

• 2

• -1/2

Why is the average rate of change negative over the interval 0 to 4?

• Because y increases as x increases

• Because y decreases as x increases

• Because x decreases as y increases

• Because both x and y decrease

What is the change in y when x changes from 0 to 4?

• 4

• 0

• 8

• -8

What is the change in x over the interval 0 to 4?

• 2

• 4

• 0

• -4

What should you do to confirm the average rate of change for other intervals?

• Guess the values

• Assume they are the same

• Calculate them

• Ignore them