[IIT 1988] Prove that f(x) is a constant if |f(x) - f(y)| is less than equal to cube |x-y|.

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Prove that f(x) is a constant if |f(x) - f(y)| is less than equal to square|x-y|. Prove that f(x) is a constant if |f(x) - f(y)| is less than equal to square|x-y|.
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f(x+y) = f(x)f(y) f(x+y) = f(x)f(y)
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Proof that sin x is smaller in magnitude than x. Proof that sin x is smaller in magnitude than x.