Question

What are the points of inflection, if any, of `f(x)=3x^5 - 5x^4`?

Answer 1

The only inflection point is `(1,-2)`.

Explanation:

An inflection point is a point on the graph at which the inflection (concavoty) changes.

`f(x) = 3x^5-5x^4`

`f'(x) = 15x^4-20x^3`

`f''(x) = 60x^3-60x^2`

`= 60x^2(x-1)`

Ths sign of `f''` changes at `x=1`, so the point `(1,f(1))` is an inflection point.