Applications Of Derivatives Question 141
Question: The value of -a- in order that $ f(x)=\sqrt{3} $ $ \sin x-\cos x-2ax+b $ decreases for all real values of x, is given by
Options:
A) $ a<1 $
B) $ a\ge 1 $
C) $ a\ge \sqrt{2} $
D) $ a<\sqrt{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
Since $ f(x)=\sqrt{3}\sin x-\cos x-2ax+b $ is decreasing for all real values of $ x, $ therefore $ f’(x)<0 $ for all x.
therefore $ \sqrt{3}\cos x+\sin x-2a<0 $ for all x
$ \Rightarrow \frac{\sqrt{3}}{2}\cos x+\frac{1}{2}\sin x<a $ for all x
therefore $ \sin ( x+\frac{\pi }{3} )<a $ for all x
therefore $ a\ge 1,,[ \because \sin ( x+\frac{\pi }{3} )\le 1 ] $ .
BETA
