# Worksheet: Tangents to the Graph of a Function

In this worksheet, we will practice finding the slope and equation of the tangent to a curve at a given point using derivatives.

**Q5: **

Find the point on the curve at which the tangent to the curve is parallel to the -axis.

- A
- B
- C
- D

**Q6: **

List the equations of all the tangents to that also lie on the point .

- A ,
- B ,
- C ,
- D ,

**Q7: **

Find the equation of the tangent to the curve that makes an angle of with the positive -axis.

- A
- B
- C
- D

**Q8: **

Suppose the line touches the curve . What is ?

**Q9: **

If the curve is tangent to the line at , find the constants and .

- A ,
- B ,
- C ,
- D ,

**Q10: **

The line touches the curve at . Find and .

- A ,
- B ,
- C ,
- D ,

**Q11: **

Do the curves and have a common tangent at the point of intersection? If so, give the equation of this tangent.

- ANo
- BYes,
- CYes,
- DYes,

**Q12: **

Determine the equation of the line tangent to the curve at point .

- A
- B
- C
- D
- E

**Q13: **

The line is tangent to the curve at the point . Find , , and .

- A , ,
- B , ,
- C , ,
- D , ,

**Q15: **

The line touches the curve at the point . Find and .

- A ,
- B ,
- C ,
- D ,

**Q16: **

Find the equation of the tangent to the curve at the point on the curve.

- A ,
- B ,
- C ,
- D ,

**Q18: **

List the equations of the normals to at the points where this curve meets the line .

- A ,
- B ,
- C ,
- D ,

**Q19: **

Determine the equation of the line normal to the curve at the point .

- A
- B
- C
- D
- E

**Q20: **

Determine the equation of the common tangent to the two curves and .

- A
- B
- C
- D

**Q22: **

Determine the equation of the tangent to the curve at the point .

- A
- B
- C
- D

**Q23: **

Find the equation of the tangent to the curve at the point with -coordinate 0.

- A
- B
- C
- D

**Q24: **

Find the equation of the tangent to the curve at .

- A
- B
- C
- D

**Q25: **

Find the equation of the normal to the curve at .

- A
- B
- C
- D