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📝 Newton’s Method

📖 From Calculus • 5. The derivative in graphing and applications • 25 questions available

Practice MCQs for Newton’s Method. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-15

7
Easy Questions
11
Medium Questions
7
Hard Questions

📝 Sample Questions

Q1. What is the iterative formula for Newton's method applied to \(f(x)=0\)?

🔹 A. \(x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}\)
🔹 B. \(x_{n+1}=x_n+\frac{f(x_n)}{f'(x_n)}\)
🔹 C. \(x_{n+1}=x_n-\frac{f'(x_n)}{f(x_n)}\)
🔹 D. \(x_{n+1}=x_n+\frac{f'(x_n)}{f(x_n)}\)

💡 Difficulty: easy | ✅ Correct: A

Q2. An offshore company wants to minimize cost \(C(x)=5x^{2}+20\ln x+30\) where \(x\) is the distance (km) from shore. Which Newton iteration formula should be used?

🔹 A. \(x_{n+1}=x_n-\frac{10x_n+20/x_n}{10+20/x_n^{2}}\)
🔹 B. \(x_{n+1}=x_n-\frac{10x_n-20/x_n}{10-20/x_n^{2}}\)
🔹 C. \(x_{n+1}=x_n-\frac{10x_n+20/x_n}{10-20/x_n^{2}}\)
🔹 D. \(x_{n+1}=x_n-\frac{10x_n-20/x_n}{10+20/x_n^{2}}\)

💡 Difficulty: medium | ✅ Correct: A

Q3. An offshore rig’s total cost is modeled by \(C(x)=0.8x^{2}+15\ln x+100\). Using Newton's method, what is the iteration formula to find the cost‑minimizing distance \(x\)?

🔹 A. \(x_{n+1}=x_n-\frac{1.6x_n+15/x_n}{1.6-15/x_n^{2}}\)
🔹 B. \(x_{n+1}=x_n-\frac{1.6x_n-15/x_n}{1.6+15/x_n^{2}}\)
🔹 C. \(x_{n+1}=x_n-\frac{1.6x_n+15/x_n}{1.6+15/x_n^{2}}\)
🔹 D. \(x_{n+1}=x_n-\frac{1.6x_n-15/x_n}{1.6-15/x_n^{2}}\)

💡 Difficulty: hard | ✅ Correct: A

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🔗 Related Topics

📝 Approximating Roots📝 Areas and Limits📝 Continuity in Applications📝 Continuity of Compositions📝 Continuity of Inverse Functions
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