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📝 Problems Involving Finite Closed Intervals

📖 From Calculus • 5. The derivative in graphing and applications • 82 questions available

Practice MCQs for Problems Involving Finite Closed Intervals. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-15

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📝 Sample Questions

Q1. For the function \(f(x)=x^2-4x+3\) on the closed interval \([0,5]\), at which point does \(f\) attain its minimum?

🔹 A. \(x=0\)

🔹 B. \(x=1\)

🔹 C. \(x=2\)

🔹 D. \(x=5\)

💡 Difficulty: easy | ✅ Correct: C

Q2. Is the function \(f(x)=|x|\) differentiable at \(x=0\) on the interval \([-3,3]\)?

🔹 A. Yes, because the slope exists

🔹 B. No, because the left‑hand derivative differs from the right‑hand derivative

🔹 C. Yes, because absolute value is smooth

🔹 D. No, because the function is not defined at 0

💡 Difficulty: medium | ✅ Correct: B

Q3. On the interval \([0,2]\), which of the following statements about the function \(f(x)=x^4-4x^3+6x^2\) is true?

🔹 A. \(f\) is decreasing on the entire interval

🔹 B. \(f\) is increasing on the entire interval

🔹 C. \(f\) has a local maximum at \(x=1\)

🔹 D. \(f\) is constant on the interval

💡 Difficulty: hard | ✅ Correct: B

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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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