Therefore, the third derivative of f is, in this case, or, using Leibniz notation, Now for a more general definition.
[1] In physics, particularly kinematics, jerk is defined as the third derivative of the position function of an object.
In mathematical terms: where j(t) is the jerk function with respect to time, and r(t) is the position function of the object with respect to time.
When campaigning for a second term in office, U.S. President Richard Nixon announced that the rate of increase of inflation was decreasing, which has been noted as "the first time a sitting president used the third derivative to advance his case for reelection.
"[2] Since inflation is itself a derivative—the rate at which the purchasing power of money decreases—then the rate of increase of inflation is the derivative of inflation, opposite in sign to the second time derivative of the purchasing power of money.
Stating that a function is decreasing is equivalent to stating that its derivative is negative, so Nixon's statement is that the second derivative of inflation is negative, and so the third derivative of purchasing power is positive.
Since Nixon's statement allowed for the rate of inflation to increase, his statement did not necessarily indicate immediate price stability but proposed a trend of more stability in the future.