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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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Solution Summary

Real functions of real variables for continuity is determined.

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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

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