Question

If $f(x)=x-2\sin x,0\le x\le 2\pi$ is increasing in the interval $[a\pi ,b\pi ]$, then find value of $a+b$.

Answer 1

Answer: 2.00

$f^{\prime }(x)=1-2\cos x\ge 0$
$\Rightarrow \cos x\le \frac{1}{2}$
$\therefore x\in \left[\frac{\pi }{3},\frac{5\pi }{3}\right]$
$\therefore a+b=\frac{1}{3}+\frac{5}{3}=2$