Question

The function $f\left(x\right)=|x^2-3x+2|+\cos \left|x\right|$ is not differentiable at $x=$

• A. -1
• B. 0
• C. 1
• D. 2

Answer 1

Answer: (C), (D)

1
2

$f\left(x\right)=|x^2-3x+2|+\cos \left|x\right|=\left|\right(x-1\left)\right(x-2\left)\right|+\cos \left|x\right|$
$\cos |x|$ is differentiable for all $x$ as $\cos \left(|x|\right)=\cos x\forall x\in R$
But $\left|\right(x-1\left)\right(x-2\left)\right|$ is not differentiable at $x=1,2$
Hence $F\left(x\right)$ is not differentiable at $x=1,2$