Question

Total number of points of non differentiability of $f(x)=$ min.$\{1,1+x^3,x^2-3x+3\}$ is ______.

Answer 1

Answer: 2

$y=x^2-3x+3$ and $y=1$,
when $x^2-3x+3=1$
or $x^2-3x+2=0$ or $x=1,2.$
$y=x^3+1$ touches
$y=1$ at $x=0$.
Further $=x^3+1$ and $y-x^2-3x+3$
intersect at only one point.
From the graph $f(x)=$ min.$\{1,1+x^3,x^2-3x+3\}$
is non-differentiable at $x=1$ and $x=2$.