# Find the intervals on which $f$ is increasing or decreasing. $f(x)=x+\cos x$ in $[0 , \pi ]$

Note: This is part 5th of a 5 part question, split as 5 separate questions here.

Toolbox:
• (i) If $f'$ is positive on an open interval $I$. Then $f$ is strictly increasing on $I$
• (ii) If $f'$ is negative on an open interval $I$, then $f$ is strictly decreasing on $I$
$f(x)=x+\cos x \;in\;[0,\pi]$
Step 1:
$f'(x)=1-\sin x$
Step 2:
Since $-1 \leq \sin x \leq 1$
$1-\sin x \geq 0 =>f'(x) \leq 0$
$\therefore$ the function is increasing in $[0, \pi]$
answered Jul 30, 2013 by