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Question
Find the values of 'a' for which the function f(x) = sin x − ax + 4 is increasing function on R ?
Solution
\[f\left( x \right) = \sin x - ax + 4\]
\[f'\left( x \right) = \cos x - a\]
\[\text { Given }:f(x) \text { is increasing on R }.\]
\[ \Rightarrow f'\left( x \right) > 0\]
\[ \Rightarrow \cos x - a > 0\]
\[ \Rightarrow \cos x > a \]
\[\text { We know,}\]
\[\cos x \geq - 1, \forall x \in R \]
\[ \Rightarrow a < - 1\]
\[ \Rightarrow a \in \left( - \infty , - 1 \right)\]
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