MonotonicityMedium
Question
The function f(x) = cos | x | - 2ax + b increases along the entire number scale. The range of ′a′ is given by-
Options
A.a = b
B.a = b/2
C.a ≤ -1/2
D.a > -3/2
Solution
f(x) = cos | x | - 2ax + b
f(x) = cos x - 2ax + b ∴[cos(-x) = cosx]
f′(x) = -sin x - 2a f′(x) ≥ 0
so -sin x - 2a ≥ 0
sin x + 2a ≤ 0 x ∈ R
1 + 2a ≤ 0 a ≤ -1/2
f(x) = cos x - 2ax + b ∴[cos(-x) = cosx]
f′(x) = -sin x - 2a f′(x) ≥ 0
so -sin x - 2a ≥ 0
sin x + 2a ≤ 0 x ∈ R
1 + 2a ≤ 0 a ≤ -1/2
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