Tangents and normals Quiz

1. Find the gradient of $y=x^2-3x$ at $x=4$.

• A. $8$
• B. $-3$
• C. $5$
• D. $13$

2. Find the equation of the tangent to $y=x^2$ at $(3,9)$.

• A. $y=6x-9$
• B. $y=6x+9$
• C. $y=9x-18$
• D. $y=3x$

3. A tangent has gradient $4$. What is the gradient of the normal at that point?

• A. $4$
• B. $-4$
• C. $\frac14$
• D. $-\frac14$

4. At which value of $x$ is the tangent to $y=x^2+2x$ parallel to $y=6x+1$?

• A. $x=1$
• B. $x=2$
• C. $x=3$
• D. $x=4$

5. Find the equation of the normal to $y=3x^2$ at $x=1$.

• A. $6x+y-9=0$
• B. $x-6y+17=0$
• C. $x+6y-19=0$
• D. $x+6y-7=0$