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📝 Relative Maxima and Minima

📖 From Calculus • 5. The derivative in graphing and applications • 31 questions available

Practice MCQs for Relative Maxima and Minima. 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. Consider \(g(x)=x^{3}-3x\). At which \(x\)-value does \(g\) have a relative maximum?

🔹 A. -1

🔹 B. 0

🔹 C. 1

🔹 D. 2

💡 Difficulty: easy | ✅ Correct: A

Q2. Find all relative extrema of \(f(x)=x^3-3x^2+2\).

🔹 A. Relative maximum at \(x=0\), minimum at \(x=2\)

🔹 B. Relative minimum at \(x=0\), maximum at \(x=2\)

🔹 C. Maximum at \(x=1\), minimum at \(x=2\)

🔹 D. No relative extrema

💡 Difficulty: medium | ✅ Correct: C

Q3. Prove that if \(f''(x)>0\) for all \(x\) in an interval, then \(f'(x)\) is increasing on that interval. Which principle justifies this?

🔹 A. Mean Value Theorem

🔹 B. Intermediate Value Theorem

🔹 C. Fundamental Theorem of Calculus

🔹 D. Rolle’s Theorem

💡 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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