The derivative of a function at a point

Consider the function $f$ whose formula is $\displaystyle f(x) = 3 - 2x$.

1. What familiar type of function is $f$? What can you say about the slope of $f$ at every value of $x$?

2. Compute the average rate of change of $f$ on the intervals $[1,4]$, $[3,7]$, and $[5,5+h]$; simplify each result as much as possible. What do you notice about these quantities?

3. Use the limit definition of the derivative to compute the exact instantaneous rate of change of $f$ with respe…

Suppose that the population, $P$, of China (in billions) can be approximated by the function $P(t) = 1.15(1.014)^t$ where $t$ is the number of years since the start of 1993.

1. According to the model, what was the total change in the population of China between January 1, 1993 and January 1, 2000? What will be the average rate of change of the population over this time period? Is this average rate of change greater or less th…