# 8.8: Instantaneous Rates of Change

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**Practice**Instantaneous Rates of Change

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Average rate of change

The average rate of change of a function is the change in coordinates of a function, divided by the change in coordinates.Average speed

The average speed of an object is the distance an object travels divided by the travel timederivative

The derivative of a function is the slope of the line tangent to the function at a given point on the graph. Notations for derivative include , , , and \frac{df(x)}{dx}.instantaneous rate of change

The instantaneous rate of change of a curve at a given point is the slope of the line tangent to the curve at that point.Instantaneous speed

The instantaneous speed of an object is the speed of the object at a specific point in time.limit

A limit is the value that the output of a function approaches as the input of the function approaches a given value.secant line

A secant line is a line that joins two points on a curve.Slope

Slope is a measure of the steepness of a line. A line can have positive, negative, zero (horizontal), or undefined (vertical) slope. The slope of a line can be found by calculating “rise over run” or “the change in the over the change in the .” The symbol for slope isTangent line

A tangent line is a line that "just touches" a curve at a single point and no others.### Image Attributions

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The difference between average rate of change and instantaneous rate of change.

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Date Created:

Nov 01, 2012
Last Modified:

Mar 23, 2016
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