$f(x)=|\log_{e} x|$ is differentiable at

$f(x)=|\log_{e} x|$ is differentiable at
  1. \(x=0\) only
  2. \(x=1\) only
  3. \(x=-1\) only
  4. \(R-\{0, \pm 1\}\)

Solution

Since the graph of $f(x)=|\log_e|x||$ has point of discontinuity at $x=0$ and the sharp edges at $x=-1$, $1$ where function is not differentiable. $f(x)=|\log_e|x||$
Hence, option (d) is correct.

Asked in: AP EAMCET 2020 (21 Sep Shift 2)

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