Question

How do you find the inflection points for the given function `f(x) = x^3 - 3x^2 + 6x`?

Answer 1

Below

Explanation:

`f(x)=x^3-3x^2+6x`
`f'(x)=3x^2-6x+6`
`f''(x)=6x-6`

Inflexion points can be found when the second derivative is equal to 0
For inflexion points, `f''(x)=0`
`6x-6=0`
`x=1`

Test `x=1` for concavity
When `x=0`, `f''(0)=-6`
When `x=1`, `f''(1)=0`
When `x=2`, `f''(2)=6`
Therefore, since there is a change in concavity, there is a point of inflexion at `(1,4)`