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in Continuity and Differentiability by (29.1k points)
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Write the set of values of k for which f(x) = kx – sin x is increasing on R.

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Best answer

f(x) = kx – Sin x

f’(x) = k – Cos x

For, f(x) to be increasing, it must have

f’(x) > 0

\(\therefore\) k – Cos x > 0

k > Cos x

Cos x < k

\(\because\) the minimum value of Cos x is 1.

Also, Cos x < k

\(\therefore\) The minimum value of k is 1.

\(\therefore\) k ∈ (1, ∞)

Hence the required set of values is k ∈ (1, ∞).

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