AP Precalculus / Unit 1: Polynomial and Rational Functions
1.2 Rates of Change
Notes
The average rate of change of $f$ on $[a,b]$ is $\displaystyle \frac{f(b)-f(a)}{b-a}$, the slope of the secant line.
- Positive rate: increasing on average. Negative: decreasing.
- Rates of change at a point can be estimated with average rates over small intervals.
Practice
$f(2)=7$ and $f(6)=19$. The average rate of change on $[2,6]$:
$\displaystyle \frac{19-7}{6-2}$.
The average rate of change is the slope of:
It connects two points on the graph.
$g(x)=x^2$. The average rate of change on $[-3,3]$:
$\displaystyle \frac{9-9}{6}=0$.
Ready for more? Take the Unit 1 test.