Applications Of Derivatives Question 255
Question: Function $ f(x)=\frac{\lambda \sin x+6\cos x}{2\sin x+3\cos x} $ is monotonic increasing, if
[MP PET 2001]
Options:
A) $ \lambda >1 $
B) $ \lambda <1 $
C) $ \lambda <4 $
D) $ \lambda >4 $
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Answer:
Correct Answer: D
Solution:
The function is monotonic increasing, if $ {f}’(x)>0 $
therefore $ \frac{(2\sin x+3\cos x),(\lambda \cos x-6\sin x)}{{{(2\sin x+3\cos x)}^{2}}} $
$ -\frac{(\lambda \sin x+6\cos x)(2\cos x-3\sin x)}{{{(2\sin x+3\cos x)}^{2}}}>0 $
therefore $ 3\lambda ({{\sin }^{2}}x+{{\cos }^{2}}x)-12({{\sin }^{2}}x+{{\cos }^{2}}x)>0 $
therefore $ 3\lambda -12>0 $
therefore $ \lambda >4. $
BETA
