4. Contextual Applications of Differentiation

Interpreting The Meaning Of The Derivative In Context — Quiz

Test your understanding of interpreting the meaning of the derivative in context with 5 practice questions.

Practice Questions

Question 1

Let $s(t)$ be the position of a particle in meters, and suppose $s'(3)=5$. What does this mean?

Question 2

Let $P(t)$ be the population of a town in thousands of people, with $t$ measured in years. If $P'(10)=-2$, what does this mean?

Question 3

Let $C(x)$ be the cost in dollars of producing $x$ items, and suppose $C'(100)=0.75$. What is the best interpretation?

Question 4

Let $d(t)$ be the depth of water in a tank in feet, and suppose $d'(4)=0$. What does this indicate at $t=4$?

Question 5

If $T(t)$ measures temperature in degrees Celsius and $t$ is measured in hours, what are the units of $T'(t)$?