📝 Tangent Lines in Derivation

📖 From Calculus • 3. The Derivation • 28 questions available

Practice MCQs for Tangent Lines in Derivation. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-13

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📝 Sample Questions

Q1. What is the slope of the tangent line to the curve \(y = x^2\) at the point \((2,4)\)?

🔹 A. \(m = 4\)

🔹 B. \(m = 2\)

🔹 C. \(m = 6\)

🔹 D. \(m = 3\)

💡 Difficulty: easy | ✅ Correct: A

Q2. For \(f(x) = \frac{1}{x}\), find \(m_{\tan}\) at \(x_0 = 2\).

🔹 A. \(m = -\frac{1}{2}\)

🔹 B. \(m = -\frac{1}{4}\)

🔹 C. \(m = \frac{1}{2}\)

🔹 D. \(m = \frac{1}{4}\)

💡 Difficulty: medium | ✅ Correct: B

Q3. The tangent line to \(y = f(x)\) at \(P(x_0,f(x_0))\) is vertical when:

🔹 A. \(m_{\tan}\) is undefined due to division by zero

🔹 B. \(f(x)\) is discontinuous at \(x_0\)

🔹 C. \(m_{\tan} = 0\)

🔹 D. \(m_{\tan}\) approaches \(\infty\)

💡 Difficulty: hard | ✅ Correct: D

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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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