Question

Function $x-\sin x$ has-

• A. a maxima
• B. a minima
• C. a maxima and a minima
• D. no maxima and no minima

Answer 1

The correct option is D no maxima and no minima

Given, $f\left(x\right)=x-\sin x$
For the interval ,$[0,\frac{\pi }{2}]$
$f\left(0\right)=0$
$f\left(\frac{\pi }{2}\right)=\frac{\pi }{2}-1$
Minimum in this interval$=0$
Maximum$=\pi$
For the interval $[\pi ,2\pi ]$
$f\left(2\pi \right)=2\pi$
Minimum in this interval$=\pi$
Maximum in this interval$=2\pi$
So, for every interval maxima and minima changes.There is no well defined maxima and minima.