Question

How do you find all points of inflection given `y=-x^5+2x^3+4`?

Answer 1

Inflection points at `x = 0` and `x = +-sqrt(5/3)`

Explanation:

Find the second derivative:

`y' = -5x^4 + 6x^2`

`y'' = -20x^3 + 12x`

This will have points of inflection when `y'' =0`.

`0 = -20x^3 + 12x`

`0 = -4x(5x^2 - 3)`

This means that `x = 0` or `x = +-sqrt(5/3)`.

Hopefully this helps!