We have,
$$y= 2x-3x^{2/3}$$
Putting $y'=0$ yields $x=1$, however the function has three intervals breaking at 1 and 0. My question is that how is the curve falling between 0 and 1 if the first derivative doesn't allow it?
2026-03-30 10:14:48.1774865688
Graph not obeying first derivative test
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The function is not differentiable at $0$. So the behavior just below zero and just above zero could be quite different (and in this case, they are quite different).