Trigonometric EquationHard
Question
Consider f(x) = cos2x(2cos2x + 3sinxcosx) + ax, where a ∈ R, Value(s) of ′a′ for which f(x) is strictly increasing for all x ∈ R can be -
Options
A.4
B.5
C.6
D.7
Solution
f(x) = 2 cos22x + 
.(2sin x cos x) cos2x + ax
⇒ f(x) = 2cos22x +
.2 sin2x cos2x + ax
⇒ f(x) = 2cos22x +
sin4x + ax
f′(x) = - 4 sin4x + 3cos4x + a ≥ 0∀ x ∈ R
⇒ a ≥ 4sin 4x - 3cos4x
⇒ a ≥ 5
.(2sin x cos x) cos2x + ax⇒ f(x) = 2cos22x +
.2 sin2x cos2x + ax⇒ f(x) = 2cos22x +
sin4x + axf′(x) = - 4 sin4x + 3cos4x + a ≥ 0∀ x ∈ R
⇒ a ≥ 4sin 4x - 3cos4x
⇒ a ≥ 5
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