Question

If $f\left(x\right)=\text{sgn}(x^2-ax+1)$ has maximum number of points of non differentiability, then

• A. $a\in (-\infty ,-2)\cup (2,\infty )$
• B. $a\in (-2,2)$
• C. $a\in (-1,1)$
• D. $a\in R$

Answer 1

The correct option is A $a\in (-\infty ,-2)\cup (2,\infty )$

For maximum points of non differnentiability of
$f\left(x\right)=\text{sgn}(x^2-ax+1),$
$x^2-ax+1=0$ must have two distinct roots,
for which $D=a^2-4>0$
$\Rightarrow a\in (-\infty ,-2)\cup (2,\infty )$