# 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.

Q1:

Given that and , find .

• A
• B
• C
• D
• E

Q2:

Given that and , find .

• A
• B
• C
• D
• E

Q3:

Given that and , find .

• A
• B
• C
• D
• E

Q4:

Given that and , determine at .

• A
• B
• C14
• D9

Q5:

Find if and .

• A
• B
• C
• D

Q6:

If and , find .

• A
• B
• C
• D

Q7:

If and , find .

• A
• B
• C
• D

Q8:

Determine , given that and .

• A
• B
• C
• D

Q9:

Given that and , find .

• A
• B
• C
• D
• E

Q10:

Given that and , find .

• A
• B
• C
• D
• E

Q11:

Given that and , find .

• A
• B
• C
• D
• E

Q12:

Given that and , find .

• A
• B
• C
• D
• E

Q13:

Given that and , determine at .

• A
• B
• C42
• D7

Q14:

Given that and , determine at .

• A
• B5
• C26
• D23

Q15:

If and , find .

• A
• B
• C
• D

Q16:

If and , find .

• A
• B
• C
• D

Q17:

If and , find .

• A
• B
• C
• D

Q18:

Given that and , find .

• A
• B
• C
• D
• E

Q19:

Given that and , find .

• A
• B
• C
• D
• E

Q20:

Given that and , find .

• A
• B
• C
• D
• E

Q21:

If and , find at .

• 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 .

• Bneither
• Cupward

Q24:

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

• Aupward
• Bdownward
• Cneither

Q25:

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

• Aupward
• Bdownward
• Cneither