Instantaneous Rate of Change
Definition
The instantaneous rate of change refers to the rate at which a function is changing at a specific point. It measures how quickly the output of a function is changing with respect to the input at that particular instant.
Analogy
Imagine you are driving a car and you want to know how fast you are going at a specific moment. The instantaneous rate of change is like looking at your speedometer and seeing your exact speed right now, rather than an average speed over a longer period of time.
Related terms
Average Rate of Change: This term refers to the overall rate at which a function changes over an interval. It calculates the total change in output divided by the total change in input.
Derivative: The derivative of a function represents its instantaneous rate of change at any given point. It gives us information about how the function is behaving locally.
Tangent Line: A tangent line to a curve represents the instantaneous rate of change at a specific point on that curve. It touches the curve only at that point and has the same slope as the curve at that point.
"Instantaneous Rate of Change" appears in:
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Additional resources (2)
Practice Questions (3)
Suppose there is a function g(x). If the value of the function at x = 3 is 4 and the derivative of the function at x = 3 is 8, what is the instantaneous rate of change of the function at the point x = 3?
What is the relationship between the average rate of change and the instantaneous rate of change?
Which of the following statements is true regarding the relationship between the average rate of change and the instantaneous rate of change of a function?
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