When the driver steps on the brakes, the speed of the car decreases. The velocity decreases with respect to time.
As a driver continues to press on the accelerator of a car, the velocity of that car continues to increase. "Acceleration" is a concept that is used to describe how velocity changes over time. Velocity and acceleration are measured using a fundamental concept of calculus that is called the derivative.
Derivatives can be used to describe the motion of many different objects. For example, derivatives have been used to describe the orbits of the planets and the descent of space shuttles. Derivatives are also used in a variety of different fields. Electrical engineers use derivatives to describe the change in current within an electric circuit. Economists use derivatives to describe the profits and losses of a given business.
The concept of a derivative is also useful for finding a tangent line to a given curve at a specific point. A tangent line is a straight line that touches a curve at only one point when restricted to a very small region. An example of a tangent line to a curve is shown in the figure. The straight line and the curve touch at only one point.
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