Question

If $xϵ(0,1)$ then $f\left(x\right)=x^{100}+\sin x-1$ is

• A. monotonic increasing
• B. monotonic decreasing
• C. not monotonic
• D. odd function

Answer 1

The correct option is A monotonic increasing

$f\left(x\right)=x^{100}+\sin x-1$
$f^{\prime }\left(x\right)=100x^{99}+\cos x$
For $x\in (0,1)$,
$f^{\prime }\left(x\right)>0$
So, $f$ is monotonic increasing