Applications Of Derivatives Question 128
Question: If the function $ f(x)=\frac{K\sin x+2\cos x}{\sin x+\cos x} $ is increasing for all values of x, then
Options:
A) $ K<1 $
B) $ K>1 $
C) $ K<2 $
D) $ K>2 $
Show Answer
Answer:
Correct Answer: D
Solution:
Since $ f(x)=\frac{K\sin x+2\cos x}{\sin x+\cos x} $ is increasing
for all x, therefore $ f’(x)>0 $ for all x
$ \Rightarrow \frac{K-2}{{{(\sin x+\cos x)}^{2}}}>0 $ for all x
therefore $ K-2>0\Rightarrow K>2 $ .
BETA
