AP Calculus BC / Unit 4: Contextual Applications of Differentiation
4.1 Interpreting the Meaning of the Derivative in Context
Notes
$f'(a)$ is the rate of change of $f$ at $a$, in units of output per input. A full interpretation names the quantity, the time or input value, the rate with units, and whether it's increasing or decreasing.
Practice
$P(t)$ is population (people) and $t$ is years. $P'(5)=-200$ means:
A negative derivative means decreasing, with units people per year.
$C(x)$ is the cost in dollars of making $x$ items. The units of $C'(x)$ are:
Output per input.
$h'(2)=0$ for the height of a ball means at $t=2$:
Zero rate of change; often the top of its path.
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