MonotonicityMedium
Question
The value of ′a′ for which the function f(x) = sin x - cosx - ax + b decreases for all real value of x, is -
Options
A.a ≥ - √2
B.a ≤ - √2
C.a ≤ √2
D.a ≥ √2
Solution
f (x) = sin x - cos x - ax + b
f′(x) = cos x + sin x - a ≤ 0 ∀ x ∈ R
⇒ a ≥ cos x + sin x ∀ x ∈ R
⇒ a ≥ √2
f′(x) = cos x + sin x - a ≤ 0 ∀ x ∈ R
⇒ a ≥ cos x + sin x ∀ x ∈ R
⇒ a ≥ √2
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