If f(x) = x² sin(1/x) for x ≠ 0 and f(0) = 0, then f′(0) equals:

If f(x) = x² sin(1/x) for x ≠ 0 and f(0) = 0, then f′(0) equals:

• A. 0
• B. 1
• C. −1
• D. Does not exist

Answer: A) 0

Explanation: f′(0) = lim(h→0) (h² sin(1/h) − 0)/h = lim(h→0) h sin(1/h) = 0 by squeeze theorem.