Q9 of 96 Page 17

Write the set of values of k for which f(x) = kx – sinx is increasing on R.

f(x) = kx – Sin x


f’(x) = k – Cos x


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


f’(x) > 0


k – Cos x > 0


k > Cos x


Cos x < k


the minimum value of Xos x is 1.


Also, Cos x < k


The minimum value of k is 1.


k ϵ (1, ∞)


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


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