Question

If $f\left(x\right)=max\{|x^2-2|x||,|x|\}$ and $g\left(x\right)=min\{|x^2-2|x||,|x|\},$ then

• A. $f\text{and}g$ are non-differentiable at $5$ points each.
• B. $f$ is non-differentiable at $5$ points while $g$ is non-differentiable at $7$ points.
• C. $f$ is non-differentiable at $7$ points while $g$ is non-differentiable at $5$ points.
• D. $f$ and $g$ are differentiable at all points.

Answer 1

The correct option is B $f$ is non-differentiable at $5$ points while $g$ is non-differentiable at $7$ points.

We can plot the graphs of $f\left(x\right)$ and $g\left(x\right)$

Graph of $f\left(x\right)$

Graph of $g\left(x\right)$

Hence, from the graph, we see that $f\left(x\right)$ is non-differentiable at $5$ points and $g\left(x\right)$ is non-differentiable at $7$ points.