Rate of Change
A rate of change can be formally defined in two ways:
where f(x) is the function with respect to x over the interval from a to a+h. An instantaneous rate of change is equivalent to a derivative.
An example to contrast the differences between the average and instantaneous definitions: the speed of a car can be calculated:
- An average rate can be calculated using the total distance travelled between a and b, divided by the travel time
- An instantaneous rate can be determined by viewing a speedometer.
Read more about this topic: Rate (mathematics)
Famous quotes containing the words rate of, rate and/or change:
“At this very moment,... the most frightful horrors are taking place in every corner of the world. People are being crushed, slashed, disembowelled, mangled; their dead bodies rot and their eyes decay with the rest. Screams of pain and fear go pulsing through the air at the rate of eleven hundred feet per second. After travelling for three seconds they are perfectly inaudible. These are distressing facts; but do we enjoy life any the less because of them? Most certainly we do not.”
—Aldous Huxley (1894–1963)
“We all run on two clocks. One is the outside clock, which ticks away our decades and brings us ceaselessly to the dry season. The other is the inside clock, where you are your own timekeeper and determine your own chronology, your own internal weather and your own rate of living. Sometimes the inner clock runs itself out long before the outer one, and you see a dead man going through the motions of living.”
—Max Lerner (b. 1902)
“Is it possible
That any may find
Within one heart so diverse mind,
To change or turn as weather and wind?
Is it possible?”
—Sir Thomas Wyatt (1503?–1542)