📝 Differentiability

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

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

🔄 Last updated: 2026-07-13

Easy Questions

Medium Questions

Hard Questions

Q1. A function \(f\) is differentiable at \(x_0\) if:

🔹 A. \(\lim_{h\to 0} \frac{f(x_0+h)-f(x_0)}{h}\) exists

🔹 B. \(\lim_{x\to x_0} f(x)\) exists

🔹 C. \(f\) is continuous at \(x_0\)

🔹 D. \(f(x_0)\) is defined

💡 Difficulty: easy | ✅ Correct: A

Q2. Is \(f(x) = x^{2/3}\) differentiable at \(x=0\)?

🔹 A. No, it has a cusp

🔹 B. Yes, derivative is 0

🔹 C. No, it's discontinuous

🔹 D. Yes, derivative exists

💡 Difficulty: medium | ✅ Correct: A

Q3. A function with a corner point is:

🔹 A. Continuous but not differentiable

🔹 B. Neither continuous nor differentiable

🔹 C. Differentiable but not continuous

🔹 D. Differentiable and continuous

💡 Difficulty: hard | ✅ Correct: A

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