Differentiation Quiz

1. Differentiate $y = 5x^3$.

• A. $15x^2$
• B. $5x^2$
• C. $15x^3$
• D. $5x^4$

2. What is $\dfrac{dy}{dx}$ if $y = 4x^2 + 6$?

• A. $8x$
• B. $8x+6$
• C. $4x$
• D. $8x^2$

3. Find the gradient of $y = 2x^2 - 3x$ at $x=1$.

• A. 1
• B. -1
• C. 4
• D. -3

4. Find the $x$-coordinate of the stationary point of $y = x^2 - 6x + 5$.

• A. 3
• B. -3
• C. 6
• D. 2

5. For $y = x^2 - 6x + 5$, the stationary point is at $x=3$. What type of stationary point is this, and why?

• A. Maximum, because gradient is positive before and negative after
• B. Minimum, because gradient is negative before and positive after
• C. Maximum, because $y$ is negative there
• D. Point of inflection, because the curve is cubic