#### Question

Find 'a' for which f(x) = a (x + sin x) + a is increasing on R ?

#### Solution

\[f\left( x \right) = a \left( x + \sin x \right) + a\]

\[f'\left( x \right) = a \left( 1 + \cos x \right)\]

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

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

\[ \Rightarrow a \left( 1 + \cos x \right) > 0 . . . \left( 1 \right)\]

\[\text { We know,}\]

\[ - 1 \leq \cos x \leq 1, \forall x \in R\]

\[ \Rightarrow 0 \leq \left( 1 + \cos x \right) \leq 2, \forall x \in R\]

\[\therefore a > 0 \left[ \text { From eq }. \left( 1 \right) \right]\]

\[ \Rightarrow a \in \left( 0, \infty \right)\]

Is there an error in this question or solution?

Solution Find 'A' for Which F(X) = a (X + Sin X) + a is Increasing on R ? Concept: Increasing and Decreasing Functions.