#### Question

Find the set of values of 'a' for which f(x) = x + cos x + ax + b is increasing on R ?

#### Solution

\[f\left( x \right) = x + \cos x + ax + b\]

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

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

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

\[ \Rightarrow 1 - \sin x + a > 0\]

\[ \Rightarrow \sin x < 1 + a\]

\[\text { We know that the maximum value of sin x is 1 }.\]

\[ \Rightarrow 1 + a > 1\]

\[ \Rightarrow a > 0\]

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

Is there an error in this question or solution?

Solution Find the Set of Values of 'A' for Which F(X) = X + Cos X + Ax + B is Increasing on R ? Concept: Increasing and Decreasing Functions.