Review on Average Rate of Change and Derivatives

Find the slope of the line that passes through the points (2, 4) and (6, 12)

• 1/2
• -1/2
• 2
• -2

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

• 2
• 1/2
• -2
• -1/2

• -4

• -1/4

• 3

• -2

What is the definition of instantaneous rate of change?

• The instantaneous rate of change is the average rate of change over a specific interval.

• The instantaneous rate of change is the rate at which a function is changing at a specific point.

• The instantaneous rate of change is the rate at which a function is changing over time.

• The instantaneous rate of change is the slope of the tangent line to the function at a specific point.

How can you find the instantaneous rate of change using limits?

• Evaluate the function at a specific point

• Integrate the function over a specific interval

• Divide the change in output by the change in input

• Take the derivative of the function

Explain the concept of average rate of change and how it relates to instantaneous rate of change.

• The average rate of change represents the rate at which the output variable changes with respect to the input variable at a specific point, while the instantaneous rate of change is the average rate of change over a specific interval.

• The average rate of change represents the rate at which the input variable changes with respect to the output variable over a specific interval, while the instantaneous rate of change is the rate of change at a specific point or instant.

• The average rate of change represents the total change in the output variable divided by the total change in the input variable, while the instantaneous rate of change is the change in the output variable divided by the change in the input variable at a specific point or instant.

• The average rate of change represents the average rate at which the output variable changes with respect to the input variable over a specific interval, while the instantaneous rate of change is the rate of change at a specific point or instant.

What is the difference between average rate of change and instantaneous rate of change?

• The average rate of change is the rate at which a quantity changes over a given interval, while the instantaneous rate of change is the average rate at which a quantity is changing at a specific point in time.

• The average rate of change is the rate at which a quantity is changing at a specific point in time, while the instantaneous rate of change is the rate at which a quantity changes over a given interval.

• The average rate of change is the average rate at which a quantity changes over a given interval, while the instantaneous rate of change is the rate at which a quantity is changing at a specific point in time or instant.

• The average rate of change is the rate at which a quantity is changing at a specific point in time, while the instantaneous rate of change is the average rate at which a quantity changes over a given interval.

• -45 gallons per minute

• -85 gallons per minute

• -15 gallons per minute

• -90 gallons per minute

Calculate the instantaneous rate of change of the function h(x) = 3x + 4 at x = 1.

• 7

• 3

• 10

• 2

Calculate the instantaneous rate of change of the function j(x) = 5x + 6 at x = 2.

• 11

• 5

• 15

• 3