📝 Concavity

📖 From Calculus • 5. The derivative in graphing and applications • 26 questions available

Practice MCQs for Concavity. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-15

Easy Questions

Medium Questions

Hard Questions

Q1. A function \(f(x)=x^3-3x\) is given. On which interval is the graph concave up?

🔹 A. \((-\infty,-1)\)

🔹 B. \((-1,1)\)

🔹 C. \((1,\infty)\)

🔹 D. \((-∞,∞)\)

💡 Difficulty: easy | ✅ Correct: C

Q2. Which of the following statements about inflection points is always true?

🔹 A. The function must be increasing at an inflection point.

🔹 B. The second derivative changes sign at an inflection point.

🔹 C. The first derivative is zero at an inflection point.

🔹 D. The function has a local maximum at an inflection point.

💡 Difficulty: medium | ✅ Correct: B

Q3. For the function \(f(x)=\frac{x}{x^2+1}\), determine the intervals of concavity.

🔹 A. Concave up for \(|x|<1\); concave down otherwise

🔹 B. Concave down for \(|x|<1\); concave up otherwise

🔹 C. Concave up for \(|x|>1\); concave down otherwise

🔹 D. Always concave up

💡 Difficulty: hard | ✅ Correct: B

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