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📝 Absolute Extrema on Open Intervals

📖 From Calculus • 5. The derivative in graphing and applications • 19 questions available

Practice MCQs for Absolute Extrema on Open Intervals. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-15

5
Easy Questions
9
Medium Questions
5
Hard Questions

📝 Sample Questions

Q1. For the cost function \(C(x)=5x^{2}-20x+30\) on the open interval \((0,5)\), which statement correctly describes its absolute extrema?

🔹 A. Absolute minimum at \(x=2\) with value \(10\); no absolute maximum.
🔹 B. Absolute maximum at \(x=2\) with value \(10\); no absolute minimum.
🔹 C. Both absolute maximum and minimum occur at the endpoints, which are not included.
🔹 D. No absolute extrema exist on the interval.

💡 Difficulty: easy | ✅ Correct: A

Q2. Given \(f(x)=x^{3}-3x\) on \((-2,2)\), what are the absolute maximum and minimum values?

🔹 A. Absolute maximum \(2\) at \(x=-1\); absolute minimum \(-2\) at \(x=1\).
🔹 B. Absolute maximum \(-2\) at \(x=1\); absolute minimum \(2\) at \(x=-1\).
🔹 C. Both extrema occur at the endpoints, which are not included.
🔹 D. No absolute extrema exist on this interval.

💡 Difficulty: medium | ✅ Correct: C

Q3. For \(f(x)=x^{4}-4x^{3}+6x^{2}\) on \((0,3)\), what can be concluded about absolute extrema?

🔹 A. The function has an absolute minimum at \(x=0\).
🔹 B. The function has an absolute maximum at \(x=3\).
🔹 C. The function has no absolute minimum or maximum on the interval.
🔹 D. Both absolute extrema occur at interior critical points.

💡 Difficulty: hard | ✅ Correct: C

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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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