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In mathematical analysis, are the differentiability of unary function and the uniform continuity of differential necessary and sufficient conditions? Is there a counterexample?
Differentiability and uniform continuity are not necessarily related.

Two counterexamples are given below.

(1) y = | x | (the absolute value of x) is obviously continuous in [- 1, 1], so it is consistent and continuous. But it's not hard to have him at 0: 00.

(2) y = x 2 is differentiable in R, but it is not uniformly continuous.

If you are satisfied, please adopt it! . ^