How can I prove that $f_n(x)=\left|x-\frac12\right|^{(n+1)/n}$ is a Cauchy sequence in $C^1[0,1]$ with sup norm? It seems obvious when we look at graphs but I need this formal way.I need this for my proof that $C^1[0,1]$ with sup norm is not a Banach space.
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