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# Solution for Find the Set of Values of 'A' for Which F(X) = X + Cos X + Ax + B is Increasing on R ? - CBSE (Science) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

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

#### Solution

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

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

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

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

$\Rightarrow 1 - \sin x + a > 0$

$\Rightarrow \sin x < 1 + a$

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

$\Rightarrow 1 + a > 1$

$\Rightarrow a > 0$

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

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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.
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