Question

$f\left(x\right)=1+\left[\cos x\right]x$ in $0<x\le \pi /2$, where $\left[\right]$ denotes greatest integer function then-

• A. it is continuous in $0<x<\pi /2$
• B. it is differentiable in $0<x<\pi /2$
• C. its maximum value is $2$
• D. it is not differentiable in $0<x<\pi /2$

Answer 1

Answer: (A), (B)

The correct options are
A it is continuous in $0<x<\pi /2$
B it is differentiable in $0<x<\pi /2$

$f\left(x\right)=1+\left[\cos x\right]x$ in $0<x\le \pi /2$
In $0<x\le \pi /2$, $cosx\in [0,1)$
$\Rightarrow f\left(x\right)=1+0.x=1$
Since $f\left(x\right)$ is a constant function, it is continuous as well as differentiable in the entire interval.