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# Solution for Write the Set of Values of K for Which F(X) = Kx − Sin X is Increasing on R ? - CBSE (Science) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

Write the set of values of k for which f(x) = kx − sin x is increasing on R ?

#### Solution

$f\left( x \right) = kx - \sin x$

$f'\left( x \right) = k - \cos x$

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

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

$\Rightarrow k - \cos x > 0$

$\Rightarrow \cos x < k$

$\text { We know that the maximum value of cosxis 1 }.$

$\text { Since cos x<k,the minimum value of k is 1 }.$

$\Rightarrow k \in \left( 1, \infty \right)$

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Solution Write the Set of Values of K for Which F(X) = Kx − Sin X is Increasing on R ? Concept: Increasing and Decreasing Functions.
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