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# 8.8: Instantaneous Rates of Change

Difficulty Level: At Grade Created by: CK-12
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### Vocabulary Language: English

Average rate of change

The average rate of change of a function is the change in $y$ coordinates of a function, divided by the change in $x$ coordinates.

Average speed

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

derivative

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 $f'(x)$, $\frac{dy}{dx}$, $y'$, $\frac{df}{dx}$ 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 $y$ over the change in the $x$.” The symbol for slope is $m$

Tangent line

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

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