Question

How do you find the inflection points of the graph of the function: `f(x)=x^4-6x^3`?

Answer 1

`x = 0, f(0) = 0 " and " x = 3, f(3) = -81`

Explanation:

A point of inflection can be found when the second derivative of f(x) is equal to zero i.e. `(d^2f)/dx^2 = 0`.

`f(x) = x^4-6x^3`
`(d^2f)/dx^2 = 12x(x-3) = 0`
`x = 0, f(0) = 0 " and " x = 3, f(3) = -81`