Differentiation Quiz

1. What is $\dfrac{dy}{dx}$ if $y = 6x^3$?

• A. $18x^2$
• B. $6x^2$
• C. $18x^3$
• D. $2x^2$

2. What does a constant term differentiate to?

• A. The constant itself
• B. 1
• C. 0
• D. $x$

3. A curve has $y = x^2 - 4x + 1$. What is the gradient of the curve at $x = 3$?

• A. $2$
• B. $6$
• C. $-4$
• D. $10$

4. A curve $y = x^2 - 6x + 5$ has a turning point where $\dfrac{dy}{dx} = 0$, at $x = 3$. Using the second derivative, what type of turning point is this?

• A. Minimum, since $\dfrac{d^2y}{dx^2} = 2 > 0$
• B. Maximum, since $\dfrac{d^2y}{dx^2} = 2 > 0$
• C. Minimum, since $\dfrac{d^2y}{dx^2} = -2 < 0$
• D. Cannot be determined

5. A particle's displacement is $s = t^3 - 3t^2$ (metres). At what time $t > 0$ is the particle momentarily at rest?

• A. $t = 1$
• B. $t = 2$
• C. $t = 3$
• D. $t = 0.5$