MCQ
$f(x) = \left\{ {\begin{array}{*{20}{c}}
  { - {x^3} + 1\,\,\,\,\,if\,\,\,\,\,\, - \infty  < x \leqslant 1} \\ 
  {|x - 1| + \lambda \,\,\,\,if\,\,\,\,\,\,\,\,\,\,\,\,x > 1} 
\end{array}} \right.$ then- 
  • A
    $ƒ(x)$ has point of minima at $x = 1\,\, \forall  \lambda  \in R$
  • B
    $ƒ(x)$ has point of minima at $x = 1$ only for $\lambda < 0$.
  • C
    $ƒ(x)$ increases at $x = 1\,\, \forall  \lambda \geq 0$
  • $ƒ(x)$ has point of minima at $x = 1\,\, \forall  \lambda > 0$

Answer

Correct option: D.
$ƒ(x)$ has point of minima at $x = 1\,\, \forall  \lambda > 0$
d
clearly $f(x)$ has point of minima at $x=1$ for $\lambda  > 0$

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