Question

Draw the graph of $y=\left|\log x\right|$

Answer 1

To draw the graph for $y=\left|\log x\right|$ we have to follow two steps:
Step $1$: Leave the positive part of $y=\log x$,as it is
Step $2$: Take the images of negative part of $y=\log x$
i.e., the part below $x-$axis in the $x-$axis as plane mirror.
The graph$\left(1\right)$ shown below $y=\log x$ is differentiable for all $x\in (0,\infty )$
The graph $\left(2\right)$ shown below $y=\left|\log x\right|$ is clearly differentiable for all $x\in (0,\infty )-\left\{1\right\}$ as at $x=1$ there is a sharp edge.