Thank you for reporting, we will resolve it shortly
Q.
Total number of points of non-differentiability of $f(x)=\min \left\{1,1+x^{3}, x^{2}-3 x+3\right\}$ is
Continuity and Differentiability
Solution:
$y=x^{2}-3 x+3$ and $y=1$,
when $x^{2}-3 x+3=1$ or $x^{2}-3 x+2$
$=0$ or $x=1,2$
$y=x^{3}+1$ touches $y=1$ at $x=0$.
Further $y=x^{3}+1$ and $y=x^{2}-3 x+3$ intersect at only one point.
From the graph $f(x)=\min \left\{1,1+x^{3}, x^{2}-3 x+3\right\}$ is non-differentiable at $x=1$ and $x=2$
