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If $f(x)=k x-\sin x$ is monotonically increasing, then
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2039 Upvotes
Verified Answer
The correct answer is:
$k>1$
Since, $f(x)=k x-\sin x$ is monotonically increasing for all $x \in R$. Therefore,
$$
f^{\prime}(x)>0 \text { for all } x \in R
$$
$\therefore \quad f^{\prime}(0)>0$
$$
\begin{array}{lr}
\Rightarrow & k-\cos 0>0 \\
\Rightarrow & k>1
\end{array}
$$
$$
f^{\prime}(x)>0 \text { for all } x \in R
$$
$\therefore \quad f^{\prime}(0)>0$
$$
\begin{array}{lr}
\Rightarrow & k-\cos 0>0 \\
\Rightarrow & k>1
\end{array}
$$
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