• # question_answer The function $f:R\to R$ is defined by $f\,(x)=-{{x}^{3}}+2a{{x}^{2}}-3bx+c,$ where a, b, $c\in R,$ is a bijective function. If $4{{a}^{2}}\le kb,$ then value of k may be A) 11 B) 13 C) 17 D) All of these

 $f\,(x)=-{{x}^{3}}+2a{{x}^{2}}-3bx+c$ $f'\,(x)=-\,3{{x}^{2}}+4a{{x}^{2}}-3b\le 0$  $\forall \,\,x$ if $16{{a}^{2}}-36b\le 0$ $4{{a}^{2}}\le 9b$     $\therefore$      $k\ge 9$