#### Question

Write the set of values of *k* for which f(x) = kx − sin x is increasing on R ?

#### Solution

\[f\left( x \right) = kx - \sin x\]

\[f'\left( x \right) = k - \cos x\]

\[\text { Forf(x) to be increasing, we must have }\]

\[f'\left( x \right) > 0\]

\[ \Rightarrow k - \cos x > 0\]

\[ \Rightarrow \cos x < k\]

\[\text { We know that the maximum value of cosxis 1 }.\]

\[\text { Since cos x<k,the minimum value of k is 1 }.\]

\[\Rightarrow k \in \left( 1, \infty \right)\]

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Solution for question: Write the Set of Values of K for Which F(X) = Kx − Sin X is Increasing on R ? concept: Increasing and Decreasing Functions. For the courses CBSE (Science), CBSE (Commerce), PUC Karnataka Science, CBSE (Arts)