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📝 Geometric Implications Of Multiplicity

📖 From Calculus • 5. The derivative in graphing and applications • 20 questions available

Practice MCQs for Geometric Implications Of Multiplicity. 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. If a polynomial \(p(x)= (x-1)^3(x+2)^2\) is graphed, what is the behavior of the graph at \(x=1\)?

🔹 A. Crosses the x‑axis with a flattening

🔹 B. Touches and turns

🔹 C. Crosses with a sharp angle

🔹 D. Remains above the axis

💡 Difficulty: easy | ✅ Correct: A

Q2. A projectile's height is modeled by \(s(t)= -5t^2 + 20t + 2\). The height becomes zero at times satisfying \((t-0.1)(t-4.9)\) (approx). What is the multiplicity of each root and what does it imply about the projectile's motion at those times?

🔹 A. Both roots have multiplicity 1; the projectile touches ground and then passes through

🔹 B. Both roots have multiplicity 1; the projectile lands and then rises again (impossible physically)

🔹 C. Each root has multiplicity 1; the projectile hits the ground at two distinct times, ascending and descending

🔹 D. One root has multiplicity 2; the projectile grazes the ground

💡 Difficulty: medium | ✅ Correct: C

Q3. Consider the function \(f(x)= (x-4)^2\). Which statement about the point \((4,0)\) on its graph is true?

🔹 A. It is a local maximum

🔹 B. The graph touches the x‑axis and turns upward

🔹 C. The graph crosses the x‑axis

🔹 D. The point is an inflection point

💡 Difficulty: easy | ✅ Correct: B

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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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