Question

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

• A. 2
• B. 3
• C. 4
• D. none of these

Answer 1

Answer: (A)

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