# What are the points of inflection of f(x)=8x + 2xsinx  on  x in [0, 2pi]?

##### 1 Answer
Jun 22, 2018

${x}_{1} \approx 1.07687398631180365861$
${x}_{2} \approx 3.6435971674254006414$

#### Explanation:

$f ' \left(x\right) = 8 + 2 \sin \left(x\right) + 2 x \cos \left(x\right)$
$f ' ' \left(x\right) = 4 \cos \left(x\right) - 2 x \sin \left(x\right)$
$f ' ' ' \left(x\right) = - 6 \sin \left(x\right) - 2 x \cos \left(x\right)$
By a numerical method we get the Solutions above.
and
$f ' ' ' \left({x}_{1}\right) \ne 0$
and
$f ' ' ' \left({x}_{2}\right) \ne 0$