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Step-by-step explanation:
Since, |f(y)−f(x)|2≤(x−y)3
⇒ |f(y)−f(x)|2(y−x)2≤(x−y)
⇒ ∣∣∣f(y)−f(x)y−x∣∣∣2≤x−y …(i)
⇒ limy→x∣∣∣f(y)−f(x)y−x∣∣∣2≤limy→x(x−y)
⇒ |f'(x)|2≤0
which is only possible, if |f'(x)|=0
∴f'(x)=0
or f'(x) = Constant
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