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# Find 'A' for Which F(X) = a (X + Sin X) + a is Increasing on R ? - CBSE (Arts) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

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

#### Solution

$f\left( x \right) = a \left( x + \sin x \right) + a$

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

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

$f'\left( x \right) > 0$

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

$\text { We know,}$

$- 1 \leq \cos x \leq 1, \forall x \in R$

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

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

$\Rightarrow a \in \left( 0, \infty \right)$

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