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๐Ÿ“ Inflection Points

๐Ÿ“– From Calculus โ€ข 5. The derivative in graphing and applications โ€ข 23 questions available

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

๐Ÿ”„ Last updated: 2026-07-15

8
Easy Questions
8
Medium Questions
7
Hard Questions

๐Ÿ“ Sample Questions

Q1. Which of the following conditions correctly characterizes an inflection point for a twiceโ€‘differentiable function \(f\)?

๐Ÿ”น A. The point where \(f'(x)=0\) and \(f''(x)>0\).
๐Ÿ”น B. The point where \(f''(x)=0\) and the concavity of \(f\) changes sign.
๐Ÿ”น C. The point where \(f'(x)=0\) and \(f''(x)=0\).
๐Ÿ”น D. The point where \(f''(x)\neq0\) but \(f'(x)=0\).

๐Ÿ’ก Difficulty: easy | โœ… Correct: B

Q2. A companyโ€™s profit function is \(P(q)= -2q^{3}+9q^{2}+15q\). At what production level \(q\) does the profit curve change concavity?

๐Ÿ”น A. \(q=0\)
๐Ÿ”น B. \(q=1.5\)
๐Ÿ”น C. \(q=3\)
๐Ÿ”น D. \(q=4.5\)

๐Ÿ’ก Difficulty: medium | โœ… Correct: C

Q3. A bridgeโ€™s loadโ€‘deflection curve is given by \(D(L)=L^{5}-5L^{3}+4L\). Determine all inflection points in the interval \([-2,2]\).

๐Ÿ”น A. \(L=-1,\,L=0,\,L=1\)
๐Ÿ”น B. \(L=-\sqrt{2},\,L=0,\,L=\sqrt{2}\)
๐Ÿ”น C. \(L=-\sqrt{5/3},\,L=\sqrt{5/3}\)
๐Ÿ”น D. No inflection points

๐Ÿ’ก Difficulty: hard | โœ… Correct: C

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๐Ÿ”— Related Topics

๐Ÿ“ Approximating Roots๐Ÿ“ Areas and Limits๐Ÿ“ Continuity in Applications๐Ÿ“ Continuity of Compositions๐Ÿ“ Continuity of Inverse Functions
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