Question

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

Answer 1

`x_1 approx 1.07687398631180365861`
`x_2 approx 3.6435971674254006414`

Explanation:

`f'(x)=8+2sin(x)+2xcos(x)`
`f''(x)=4cos(x)-2xsin(x)`
`f'''(x)=-6sin(x)-2xcos(x)`
By a numerical method we get the Solutions above.
and
`f'''(x_1)ne 0`
and
`f'''(x_2) ne 0`