📝 DIFFERENTIABILITY OF FUNCTIONS DEFINED IMPLICITLY

📖 From Calculus • 4. Topics in Differentiation • 26 questions available

Practice MCQs for DIFFERENTIABILITY OF FUNCTIONS DEFINED IMPLICITLY. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-14

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📝 Sample Questions

Q1. When differentiating implicitly, what assumption is made about \(y\)?

🔹 A. \(y\) is a constant

🔹 B. \(y\) is always positive

🔹 C. \(y\) represents a differentiable function of \(x\)

🔹 D. \(y\) is independent of \(x\)

💡 Difficulty: easy | ✅ Correct: C

Q2. For the equation \(x^2 + y^2 + 1 = 0\), implicit differentiation gives \(\frac{dy}{dx} = -\frac{x}{y}\). Why is this result meaningless?

🔹 A. Because \(y\) is not a function of \(x\)

🔹 B. Because the derivative should be positive

🔹 C. Because the equation is not differentiable

🔹 D. Because no real values of \(x\) and \(y\) satisfy the equation

💡 Difficulty: medium | ✅ Correct: D

Q3. For the equation \(x^3 + y^3 = 3xy\), the derivative \(\frac{dy}{dx} = \frac{y - x^2}{y^2 - x}\) is undefined when:

🔹 A. \(y^2 = x\)

🔹 B. \(x = y^2\)

🔹 C. \(x^2 = y\)

🔹 D. \(y = x^2\)

💡 Difficulty: hard | ✅ Correct: A

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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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