# Worksheet: Second Derivatives of Parametric Equations

In this worksheet, we will practice finding second derivatives and higher-order derivatives of parametric equations by applying the chain rule.

**Q3: **

Given that and , find .

- A
- B
- C
- D
- E

**Q4: **

Given that and , determine at .

**Q5: **

Find if and .

- A
- B
- C
- D

**Q7: **

If and , find .

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- B
- C
- D

**Q8: **

Determine , given that and .

- A
- B
- C
- D

**Q12: **

Given that and , find .

- A
- B
- C
- D
- E

**Q13: **

Given that and , determine at .

**Q14: **

Given that and , determine at .

**Q17: **

If and , find .

- A
- B
- C
- D

**Q18: **

Given that and , find .

- A
- B
- C
- D
- E

**Q20: **

Given that and , find .

- A
- B
- C
- D
- E

**Q22: **

Consider the parameric curve and . Determine whether this curve is concave up, down, or neither at .

- Aneither
- Bupward
- Cdownward

**Q23: **

Consider the parameric curve and . Determine whether this curve is concave up, down, or neither at .

- Adownward
- Bneither
- Cupward

**Q25: **

Consider the parameric curve and . Determine whether this curve is concave up, down, or neither at .

- Aupward
- Bdownward
- Cneither