3. Calculus Foundations

Applications — Quiz

Test your understanding of applications with 5 practice questions.

Practice Questions

Question 1

What is the first step in solving an optimization problem using derivatives?

Question 2

A rectangular garden is to be fenced on three sides using 100 meters of fencing, with one side along a wall that requires no fencing. What is the function for the area of the garden in terms of its width $w$?

Question 3

Which of the following is the correct interpretation of a critical point of a function $f(x)$?

Question 4

A particle moves along a line, and its position at time $t$ is given by $s(t) = 3t^3 - 9t^2 + 6t$. At what times is the particle at rest?

Question 5

If $f(x) = x^3 - 3x^2 - 9x + 5$, what is the second derivative $f''(x)$?