# Lesson Worksheet: Second Derivatives of Parametric Equations Mathematics • Higher Education

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 .

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• E

Q2:

Given that and , find .

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Q3:

Given that and , find .

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Q4:

Given that and , determine at .

Q5:

Find if and .

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Q6:

If and , find .

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Q7:

If and , find .

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Q8:

Determine , given that and .

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Q9:

Given that and , find .

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Q10:

Given that and , find .

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Q11:

Given that and , find .

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Q12:

Given that and , find .

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Q13:

Given that and , determine at .

Q14:

Given that and , determine at .

Q15:

If and , find .

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Q16:

If and , find .

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Q17:

If and , find .

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Q18:

Given that and , find .

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Q19:

Given that and , find .

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Q20:

Given that and , find .

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Q21:

If and , find at .

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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