← Back to 2. Limits and Continuity an Introduction

📝 Intermediate-Value Theorem

📖 From Calculus • 2. Limits and Continuity an Introduction • 30 questions available

Practice MCQs for Intermediate-Value Theorem. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-12

Easy Questions

Medium Questions

Hard Questions

📝 Sample Questions

Q1. What does the Intermediate-Value Theorem (IVT) state?

🔹 A. If \(f\) is continuous on \([a,b]\), then \(f\) takes every value between \(f(a)\) and \(f(b)\)

🔹 B. If \(f\) is continuous on \([a,b]\), then \(f(a)=f(b)\)

🔹 C. If \(f\) is differentiable on \([a,b]\), then \(f\) takes every value

🔹 D. If \(f\) is continuous on \((a,b)\), then \(f\) is bounded

💡 Difficulty: easy | ✅ Correct: A

Q2. The IVT guarantees the existence of a solution to \(f(x)=0\) if:

🔹 A. \(f\) is continuous on \([a,b]\) and \(f(a)f(b)<0\)

🔹 B. \(f\) is differentiable on \([a,b]\)

🔹 C. \(f\) is increasing on \([a,b]\)

🔹 D. \(f(a)=f(b)=0\)

💡 Difficulty: medium | ✅ Correct: A

Q3. If \(f\) is continuous on \([a,b]\) and \(f(a)\) and \(f(b)\) have opposite signs, then:

🔹 A. There is at least one root in \((a,b)\)

🔹 B. There is no root in \((a,b)\)

🔹 C. There is exactly one root in \((a,b)\)

🔹 D. There are infinitely many roots

💡 Difficulty: easy | ✅ Correct: A

⬆️ View all questions in the quiz below

🔗 Related Topics

📝 Approximating Roots 📝 Areas and Limits 📝 Continuity in Applications 📝 Continuity of Compositions 📝 Continuity of Inverse Functions

🚀 Start Quiz 📝 Practice Mode