Inequalities doubt

[Halflife]

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[eco'17]

I'm not sure about this answer but we can go about doing this question like this!
|f(x)-f(y)|/|x-y|<=|x-y|^2
as both lhs and rhs has to be positive therefore this implies f'(x)=0
therefore the function is a constant

[Halflife]

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[Halflife]

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