# Verify Rolles theorem for the function $f(x)=\sin 2x \;in\;\bigg[0,\Large\frac{\pi}{2}\bigg]$

Toolbox:
• Check $f$ is continuous and differentiable in $\bigg[ 0, \large\frac{\pi}{2} \bigg]$ and $f(0)=f\bigg( \large\frac{\pi}{2} \bigg)$
• Then find C
$f$ is continuous and differentiable.
$f(0)=f\bigg( \large\frac{\pi}{2}\bigg) = a$
$\Rightarrow \exists$ a point $C \in \bigg( 0,\large \frac{\pi}{2} \bigg)$

$f ' (C)=0$
$f ' (x)=2cos2x = 0$
$\Rightarrow x = \large\frac{\pi}{4} \in \bigg( 0,\large \frac{\pi}{2} \bigg)$
$C = \large\frac{\pi}{4}$

edited Mar 26, 2013