Question

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

Answer 1

`f(x)=8x+3-2 sinx`

`f'(x)=8-2 cosx`

`f''(x)= 2 sinx`

`f''(x) =2sinx = 0` at every integer multiple of `pi` and, we know the sine changes sign at every `x` intercept,

so every point:
`(n pi,0)` with integer `n` is an inflection point.