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📝 Absolute Extrema On Infinite Intervals

📖 From Calculus • 5. The derivative in graphing and applications • 24 questions available

Practice MCQs for Absolute Extrema On Infinite 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. Which of the following best describes an absolute maximum of a function \(f\) on the interval \((-\infty,\infty)\)?

🔹 A. A point where \(f'(x)=0\) and the function changes from increasing to decreasing

🔹 B. The largest function value attained at some \(x\) in the interval

🔹 C. A point where the limit of \(f(x)\) as \(x\to\infty\) is finite

🔹 D. A point where \(f\) is undefined

💡 Difficulty: easy | ✅ Correct: B

Q2. A company wants to minimize the cost \(C(x)=5x+200e^{-0.1x}\) where \(x\) represents production units (with \(x\ge0\)). Which value of \(x\) gives the absolute minimum cost?

🔹 A. \(x=0\)

🔹 B. \(x=10\)

🔹 C. \(x=20\)

🔹 D. \(x= \displaystyle\frac{200}{5}\)

💡 Difficulty: medium | ✅ Correct: B

Q3. A cost function is \(C(x)=x^2+4x+7\) for \(x\ge -2\). Does \(C\) have an absolute minimum on this interval?

🔹 A. Yes, at \(x=-2\)

🔹 B. Yes, at \(x=-1\)

🔹 C. No absolute minimum exists

🔹 D. It has both a minimum and maximum

💡 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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