Let f:R→R be a function defined by f(x)=max{x,x2}. Let S denote the set of all points in R where f is not differentiable. Then:
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Official solution
\[f(x)=⎩⎨⎧x2,x,x2,x<00≤x<1x≥1\]
The pieces cross with different slopes at x=0 (slope 0 vs 1) and x=1 (slope 1 vs 2), so f is not differentiable at x=0,1.