Q93 / 150 · MHT CET 2007 · Mathematics

If $f(x)=k x-\sin x$ is monotonically increasing, then

  • Correct answer
    A
    $k>1$
  • B
    $k>-1$
  • C
    $k < 1$
  • D
    $k < -1$

Solution

Since, $f(x)=k x-\sin x$ is monotonically increasing for all $x \in R$. Therefore, $$ f^{\prime}(x)>0 \text { for all } x \in R $$ $\therefore \quad f^{\prime}(0)>0$ $$ \begin{array}{lr} \Rightarrow & k-\cos 0>0 \\ \Rightarrow & k>1 \end{array} $$

Hence, the correct answer is option: 'A'.

Relevant Questions