5.14 Implicit differentiation, related rates and optimisation Quiz

1. Find $\dfrac{dy}{dx}$ for $x^{3} + y^{3} = 9$.

• A. $-\dfrac{x^{2}}{y^{2}}$
• B. $\dfrac{x^{2}}{y^{2}}$
• C. $-\dfrac{y^{2}}{x^{2}}$
• D. $-3x^{2}$

2. For $xy = 6$, find $\dfrac{dy}{dx}$ at $(2, 3)$.

• A. $-\dfrac{2}{3}$
• B. $\dfrac{3}{2}$
• C. $-\dfrac{3}{2}$
• D. $-6$

3. The side of a cube increases at $0.1\text{ cm s}^{-1}$. How fast is the volume increasing when the side is $10$ cm?

• A. $30\text{ cm}^{3}\text{ s}^{-1}$
• B. $300\text{ cm}^{3}\text{ s}^{-1}$
• C. $100\text{ cm}^{3}\text{ s}^{-1}$
• D. $3\text{ cm}^{3}\text{ s}^{-1}$

4. $f(x) = x^{2} - 6x$ on $0 \le x \le 2$. Where is the minimum value of $f$?

• A. $x = 3$
• B. $x = 0$
• C. $x = 2$
• D. $x = 1$

5. A $5$ m ladder slides so that its foot moves away from a wall at $0.3\text{ m s}^{-1}$. How fast is the top sliding down when the foot is $3$ m from the wall?

• A. $0.4\text{ m s}^{-1}$
• B. $0.3\text{ m s}^{-1}$
• C. $0.225\text{ m s}^{-1}$
• D. $0.18\text{ m s}^{-1}$