Applications Of Derivatives Question 430
Question: The function $ f(x)=1+x(\sin x)[\cos x],0<x\le \frac{\pi }{2} $ (where [.] is G.I.F.)
Options:
A) Is continuous on $ ( 0,\frac{\pi }{2} ) $
B) Is strictly increasing in $ ( 0,\frac{\pi }{2} ) $
C) Is strictly decreasing in $ ( 0,\frac{\pi }{2} ) $
D) Has global maximum value 2
Show Answer
Answer:
Correct Answer: A
Solution:
[a] For $ 0<x\le \frac{\pi }{2};[\cos x]=0 $
Hence, $ f(x)=1 $ for all $ ( 0,\frac{\pi }{2} ] $
Trivially f(x) is continuous on $ ( 0,\frac{\pi }{2} ) $
This function is neither strictly increasing nor strictly decreasing and its global maximum is 1.
BETA
