5.4 Tangents and normals Quiz

1. The tangent to a curve at a point has gradient $4$. What is the gradient of the normal there?

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

2. Find the equation of the tangent to $y=x^2+1$ at the point $(1,2)$.

• A. $y=2x$
• B. $y=2x+1$
• C. $y=x+1$
• D. $y=-\frac12x+\frac52$

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

• A. $y=-2x+3$
• B. $y=2x-1$
• C. $y=\frac12x+\frac12$
• D. $y=-\frac12x+\frac32$

4. A tangent to a curve is horizontal at $x=3$. What is the equation of the normal there?

• A. $y=3$
• B. $y=0$
• C. $x=3$
• D. $x=0$

5. For $y=x^3-3x$, at which values of $x$ is the tangent parallel to $y=9x+2$?

• A. $x=\pm2$
• B. $x=3$
• C. $x=\pm\sqrt3$
• D. $x=0$