# What are the points of inflection of f(x)=xcosx  on the interval x in [0,2pi]?

$f ' \left(x\right) = \cos \left(x\right) - x \sin \left(x\right)$
f"(x)=-2sin(x)-xcos(x)
set f"(x)=0 for points of inflection, x=0, 2.29
On your calculator let equation 1 be $y = 2 \sin \left(x\right)$
let equation 2 be $y = - x \cos \left(x\right)$
Find the points of intersection in $\left[0 , 2 \pi\right]$