1. Calculus Foundations

Applications Of Derivatives — Quiz

Test your understanding of applications of derivatives with 5 practice questions.

Practice Questions

Question 1

A rectangular box with a square base has a volume of $V = 1000 \text{ cm}^3$. If the side length of the base is $x$ and the height is $h$, which of the following expressions represents the surface area of the box to be minimized?

Question 2

A ladder $5 \text{ m}$ long is leaning against a wall. If the bottom of the ladder is pulled away from the wall at a rate of $0.5 \text{ m/s}$, how fast is the top of the ladder sliding down the wall when the bottom is $3 \text{ m}$ from the wall?

Question 3

For a function $f(x)$, if $f'(x) = (x-1)^2 (x-3)$, at what value(s) of $x$ does $f(x)$ have a local minimum?

Question 4

Consider the function $f(x) = x^4 - 4x^3$. At what interval(s) is the function concave up?

Question 5

A farmer has $1200 \text{ ft}$ of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that will maximize the area?