Question

Let f(x) = (x² – 4) |(x – 1) (x – 2) (x – 3)| + $\frac{\sin(\mathcal{l}nx)}{1 + |\sin(\mathcal{l}nx)|}$ the set of points at which the function f(x) is not differentiable is –

• A. $\left\{ \frac{1}{2},2,1,3 \right\}$
• B. $\left\{ \frac{1}{2},3 \right\}$
• C. $\left\{ \frac{1}{2},2 \right\}$
• D. {1, 3}

Answer 1

Answer: (D)

{1, 3}

Answer 2

$\frac{\sin(\mathcal{l}nx)}{1 + |\sin(\mathcal{l}nx)|}$ is differentiable for all values of x and (x² – 4) |(x – 1) (x – 2) (x – 3)| is differentiable for all values of x except x = 1, 3.