Is the sequence of functions uniformly convergent if we know that the derivative of $f$ with respect to $x$ exist for all $x$ in the domain of interest.
$$f_n=\frac{f(x+\frac{1}{n})-f(x)}{\frac{1}{n}}$$
If so, how does one prove this?
2026-04-29 09:42:39.1777455759
Is $f_n=\frac{f(x+\frac{1}{n})-f(x)}{\frac{1}{n}}$ uniformly convergent?
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The answer is No in general
Hint: think about a differentiable function which is not continuously differentiable