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📝 Endpoint Derivatives

📖 From Calculus • 3. The Derivation • 26 questions available

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

🔄 Last updated: 2026-07-13

8
Easy Questions
11
Medium Questions
7
Hard Questions

📝 Sample Questions

Q1. What is the left-hand derivative of \(f\) at \(x\)?

🔹 A. \(f'_-(x) = \lim_{h\to 0^-} \frac{f(x+h)-f(x)}{h}\)
🔹 B. \(f'_-(x) = \lim_{h\to 0^+} \frac{f(x+h)-f(x)}{h}\)
🔹 C. \(f'_-(x) = \lim_{h\to 0} \frac{f(x-h)-f(x)}{h}\)
🔹 D. \(f'_-(x) = \lim_{h\to 0} \frac{f(x)-f(x+h)}{h}\)

💡 Difficulty: easy | ✅ Correct: A

Q2. For \(f(x) = \sqrt{x}\) on \([0,4]\), what is \(f'_+(0)\)?

🔹 A. Undefined (infinite)
🔹 B. 0
🔹 C. 1
🔹 D. \(\frac{1}{2}\)

💡 Difficulty: medium | ✅ Correct: A

Q3. If \(f\) is differentiable on \([a,b]\), then \(f'_+(a)\):

🔹 A. Exists as a finite number
🔹 B. May be infinite
🔹 C. Does not exist
🔹 D. Is always 0

💡 Difficulty: hard | ✅ Correct: A

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🔗 Related Topics

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