# Worksheet: Slope of a Polar Curve

In this worksheet, we will practice finding the slope of a polar curve at a point and sketching this curve along with its tangent at that point.

**Q1: **

Find the slope of the tangent line to the curve at .

- A
- B0
- C
- D
- E

**Q2: **

Find the slope of the tangent line to the polar curve at the point .

- A
- B
- C0
- D

**Q3: **

Find the slope of the tangent line to the curve at .

- A
- B
- C
- D
- E

**Q4: **

Find the slope of the tangent line to the curve at .

- A
- B
- C
- D
- E

**Q5: **

Find the slope of the tangent line to the curve at .

- A
- B
- C0
- D
- E

**Q6: **

Find the slope of the tangent line to the curve at .

- A
- B
- C
- D
- E

**Q7: **

Find the slope of the tangent line to the polar curve at the point .

- A
- B
- C
- D
- E

**Q8: **

Find the slope of the tangent line to the curve at .

- A
- B
- C
- D
- E

**Q9: **

Find the slope of the tangent line to at . Round your answer to 3 decimal places.

**Q10: **

Find the slope of a tangent line to at .

- A4
- B0
- C−1
- DThe slope is undefined at .
- E1

**Q11: **

Find the slope of a tangent line to at .

- A
- B
- C
- D
- E

**Q12: **

Find the slope of a tangent line to at .

**Q13: **

Find the slope of the tangent line to at the point .

**Q14: **

Find the slope of the tangent line to at . Give your answer to 3 decimal places.

**Q15: **

For the cardioid , find the slope of the tangent line at .

**Q16: **

Find the points at which has a horizontal or vertical tangent line.

- ANo horizontal tangents, vertical tangents at and
- BHorizontal tangents at and , vertical tangents at and
- CHorizontal tangents at and , vertical tangents at and
- DHorizontal tangents at and , vertical tangents at and
- EHorizontal tangents at , no vertical tangents

**Q17: **

Given a polar curve defined by , form an expression for the slope of the curve in terms of and .

- A
- B
- C
- D
- E

**Q18: **

Find the slope of the tangent line to at .

- A
- B
- C1
- D
- EThe slope of the tangent line is undefined.

**Q19: **

Find the slope of the tangent line to at the point .

- A
- B0
- C
- D
- E

**Q20: **

Find the slopes of the tangent lines to at the tips of the leaves.

- AThe slope is at , at , and undefined at .
- BThe slope is 0 at the tips of all the leaves.
- CThe slope is at , at , and 0 at .
- DThe slope is at , at , and 0 at .
- EThe slope is at , at , and 0 at .

**Q21: **

Find the slopes of the tangent lines to at the tips of the leaves.

- AThe slope is 1 at and and the slope is at and .
- BThe slope is 0 at and and the slope is undefined at and .
- CThe slope is 0 at the tips of all the leaves.
- DThe slope is undefined at and and the slope is 0 at and .
- EThe slope is undefined at the tips of all the leaves.

**Q22: **

Find the slope of the tangent line to the curve at .

- A
- B0
- C
- D
- E

**Q23: **

Find the slope of the tangent line to the polar curve at the point .

- A
- B
- C
- D
- E

**Q24: **

Find the slope of the tangent line to the curve at .

- A
- B
- C1
- D

**Q25: **

Find the slope of the tangent line to the curve at .

- A2
- B1
- C
- D
- E