# How do you find the inflection points for the function f(x)=8x+3-2 sinx?

Apr 24, 2015

$f \left(x\right) = 8 x + 3 - 2 \sin x$

$f ' \left(x\right) = 8 - 2 \cos x$

$f ' ' \left(x\right) = 2 \sin x$

$f ' ' \left(x\right) = 2 \sin x = 0$ at every integer multiple of $\pi$ and, we know the sine changes sign at every $x$ intercept,

so every point:
$\left(n \pi , 0\right)$ with integer $n$ is an inflection point.