MonotonicityHard
Question
Function f(x) = 
is monotonic increasing when-
is monotonic increasing when-Options
A.λ < 1
B.λ > 1
C.λ < 2
D.λ > 2
Solution
f(x) = 
(2 sin x + 6 cos x ) [λ cos x - 3 sin x)
f′(x)
> 0
2λ(sin x cos x ) - 6 sin2 x + 6λ cos2 x - 18 sin x cos x
=
> 0
2λ sin x cos x - 6 sin2 x + 6λ cos2 x - 18 sin x cos x
=
> 0
> 0 6λ > 6 λ > 1
(2 sin x + 6 cos x ) [λ cos x - 3 sin x)
f′(x)
> 02λ(sin x cos x ) - 6 sin2 x + 6λ cos2 x - 18 sin x cos x
=
> 02λ sin x cos x - 6 sin2 x + 6λ cos2 x - 18 sin x cos x
=
> 0> 0 6λ > 6 λ > 1Create a free account to view solution
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