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Question: Function f(x) = \(\frac{\lambda\sin x + 6\cos x}{2\sin x + 3\cos x}\) monotonic increasing if...

Function f(x) = λsin⁡x+6cos⁡x2sin⁡x+3cos⁡x\frac{\lambda\sin x + 6\cos x}{2\sin x + 3\cos x} monotonic increasing if

A

l> 1

B

l< 1

C

l< 4

D

l> 4

Answer

l> 4

Explanation

Solution

Q we know that f(x) = asin⁡x+bcos⁡xcsin⁡x+dcos⁡x\frac{a\sin x + b\cos x}{c\sin x + d\cos x} is

Monotonically increasing if ad – bc > 0 & monotonically decreases if ad – bc < 0

\ from the Q. f(x) is monotonically increasing If 3l – 12 > 0 Ž l > 4