<meta http-equiv="refresh" content="1; url=/nojavascript/">
You are viewing an older version of this Concept. Go to the latest version.

# Instantaneous Rates of Change

## Derivative is the slope of the tangent line at a point.

0%
Progress
Practice Instantaneous Rates of Change
Progress
0%
Instantaneous Rates of Change

### Vocabulary Language: English

Average rate of change

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

Average speed

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

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

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

Instantaneous speed

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

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

secant line

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

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

Tangent line

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