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# Solution for Find the Set of Values of 'B' for Which F(X) = B (X + Cos X) + 4 is Decreasing on R ? - CBSE (Commerce) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

Find the set of values of 'b' for which f(x) = b (x + cos x) + 4 is decreasing on R ?

#### Solution

$f\left( x \right) = b\left( x + \cos x \right) + 4$

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

$\text { Given }:f(x) \text { is decreasing on R }.$

$\Rightarrow f'\left( x \right) < 0$

$\Rightarrow b\left( 1 - \sin x \right) < 0 . . . \left( 1 \right)$

$\text { We know },$

$\sin x \leq 1$

$\Rightarrow 1 - \sin x \geq 0$

$\Rightarrow b < 0 \left[ \text { Since } \left( 1 - \sin x \right) \geq 0, b\left( 1 - \sin x \right) < 0 \Rightarrow b < 0 \right]$

$\Rightarrow b \in \left( - \infty , 0 \right)$

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Solution Find the Set of Values of 'B' for Which F(X) = B (X + Cos X) + 4 is Decreasing on R ? Concept: Increasing and Decreasing Functions.
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