MCQ
Let $f(x) = \left[ {\begin{array}{*{20}{c}}
  {a{{\cot }^{ - 1}}\left( {\frac{{b + x}}{4}} \right),\,\,\frac{{ - 2}}{3}\, < \,x\, < \,0} \\ 
  {2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,x = 0} \\ 
  {\frac{{\ln (1 - cx)}}{x},\,0\, < \,x\, < \,\frac{2}{3}} 
\end{array}} \right.$ If the function $f(x)$ is differentiable at $x = 0,$ then find the value of $(b^2 -2a + c^6).$
  • A
    $18$
  • B
    $38$
  • C
    $0$
  • $48$

Answer

Correct option: D.
$48$
d

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