BUS 111 Lecture Notes - Lecture 6: Pc100, If And Only If, Ath
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Def: givin a function f(x) and two x-values, a and b, the average rate of change is given by: Example: suppose that the population of a particular demographic is modeled by: P(t)=(1. 27)t, where t is the time after the year 2000. Meaning that, on average, each year the population increases by about 5. Often, we care about how things are changing right now. For this we need an instantaneous rate of change. In order to do this, we need a and b to be close together. If a is a number, we want b to be something like a+0. 1. Call this a+h, where h is (cid:498)really small(cid:499). f(a+h) f(a) We can define the instantaneous rate of change of a function f(x) at the point x+a as: Example: find the instantaneous rate of change of f(x)=3x2-10 at x=1. This means that if x increases by 1, f(x) increases by 6.
