Applications Of Derivatives Question 344
Question: The function $ \sin x-\cos x $ is increasing in the interval
Options:
A) $ [ \frac{3\pi }{4},\frac{7\pi }{4} ] $
B) $ [ 0,\frac{3\pi }{4} ) $
C) $ [ \frac{\pi }{4},\frac{3\pi }{4} ] $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
We have, $ f’(x)=\cos x+\sin x $
Now $ f(x) $ is increasing function of x, if $ f’(x)=\cos x+\sin x>0 $ or $ \sqrt{2}\cos ( x-\frac{\pi }{4} )>0 $
therefore $ 0\le x<\frac{3\pi }{4}i.e.,f’(x)>0 $ in $ [ 0,\frac{3\pi }{4} ) $ .
BETA
