2. Pure Calculus

Applications Derivatives — Quiz

Test your understanding of applications derivatives with 5 practice questions.

Practice Questions

Question 1

The displacement $s$ of a particle (in meters) at time $t$ (in seconds) is given by $s(t) = t^2 - 4t + 7$. What is the initial velocity of the particle?

Question 2

Find the $x$-coordinate of the stationary point of the curve $y = 3x^2 - 12x + 10$.

Question 3

The area $A$ of a square is increasing at a rate of $8 \text{ cm}^2/\text{s}$. At what rate is the side length $s$ of the square increasing when the side length is $4 \text{ cm}$?

Question 4

For the function $f(x) = x^3 - 3x^2 + 5$, determine the nature of the stationary point at $x = 0$.

Question 5

A rectangular field is to be enclosed by $100$ meters of fencing. What is the maximum possible area of the field?