Question

The function $f(x) = 1 + x(\sin\, x)[\cos\, x], 0 < x \leq \frac{\pi}{2}$ (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 $0 < x \leq \frac{\pi}{2} ;[\cos \,x]=0$
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 .