Question

The function $f(x)=1+x(\sin x)[\cos x],0<x\le \frac{\pi }{2}$ (where [.] is G.I.F.)

• A. is continuous on $\left(0,\frac{\pi }{2}\right)$
• B. is strictly increasing in $\left(0,\frac{\pi }{2}\right)$
• C. is strictly decreasing in $\left(0,\frac{\pi }{2}\right)$
• D. has global maximum value 2

Answer 1

Answer: (A)

For $0<x\le \frac{\pi }{2};[\cos x]=0$
Hence, $f(x)=1$ for all $\left(0,\frac{\pi }{2}\right]$
Trivially $f(x)$ is continuous on $\left(0,\frac{\pi }{2}\right)$
This function is neither strictly increasing nor strictly decreasing and its global maximum is 1 .