AP Calculus AB / Unit 4: Contextual Applications of Differentiation
4.3 Rates of Change in Applied Contexts Other Than Motion
Notes
Derivatives describe any rate: water flowing, temperature changing, cost per item, population growth. The second derivative tells whether that rate is itself increasing or decreasing.
Practice
$W(t)$ is gallons of water in a tank. $W'(t)>0$ and $W''(t)<0$ means:
Increasing amount, decreasing rate.
$T(10)=68$ and $T'(10)=-1.5$ (°F, minutes). Which is true?
Read the sign and units of the derivative.
Marginal cost in economics is:
It's the rate of change of cost per extra item.
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