Find the set of values of ‘b’ for which f(x) = b(x + cosx) + 4 is decreasing on R.
f(x) = b (x + Cos x) + 4
f’(x) = b (1 – Sin x) + 0
f’(x) = b (1 – Sin x)
f(x) is decreasing on R.
f’(x) < 0
b (1 – Sin x) < 0
Sin x ≤ 1
1 – Sin x ≥ 0
b (1 – Sin x) < 0 & 1 – Sin x ≥ 0
b < 0
b ϵ (-∞, 0)
Hence the required set of values is b ϵ (-∞, 0).
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