Question

What are the points of inflection, if any, of `f(x) =12x^5+15x^4–240x^3+6`?

Answer 1

The points of inflection are at:
`x=0,(-3+-sqrt(393))/8`

Explanation:

The points of inflection are given by when `f''(x)=0`.

`f(x)=12x^5+15x^4-240x^3+6`
`f'(x) =60x^4+60x^3-720x^2`
`f''(x)=240x^3+180x^2-1440x`

`x=60x(4x^2+3x-24)`
(1)
`60x=0`
`x=0`

(2) and (3)
`4x^2+3x-24=0`
`x=(-3+-sqrt(393))/8`