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Let f:R->R satisfy |f(t)-f(x)|<=|t-x|^2 for any t,x.
Prove that (f) is constant.

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Please see attachment.

We don't know anything about function (f), whether it is or it is not continuous, differentiable etc.
We just know that the above inequality is valid for any values of (t) and (x).
Let's consider the special case when