Continuity and DifferentiabilityHard

Question

If f is a real-valued differentiable function satisfying | f(x) - f(y) | ≤ (x - y)2, x, y ∈ R and f(0) = 0, then f(1) equals

Options

A.1
B.2
C.0
D.-1

Solution

| f(x + h) - f(x) | ≤ (x + h - x)2
⇒ ≤ 0 ⇒ f′(x) = 0
⇒ f(x) is constant function   ⇒ f(1) = 0

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