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in Continuity and Differentiability by (29.3k points)
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Find the vales of ‘a’ for which the function f(x) = sin x – ax + 4 is increasing function on R.

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f(x) = Sin x – ax + 4

f’(x) = Cos x – a + 0

f’(x) = Cos x – a

\(\because\) f(x) is increasing on R.

f’(x) > 0

\(\therefore\) Cos x – a > 0

Cos x > a

\(\because\) Cos x ≥ -1, ∀ x ∈ R

\(\therefore\) a < -1

\(\therefore\) a ∈ (-∞, -1)

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

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