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

$x = 0 , f \left(0\right) = 0 \text{ and } x = 3 , f \left(3\right) = - 81$
A point of inflection can be found when the second derivative of f(x) is equal to zero i.e. $\frac{{d}^{2} f}{\mathrm{dx}} ^ 2 = 0$.
$f \left(x\right) = {x}^{4} - 6 {x}^{3}$
$\frac{{d}^{2} f}{\mathrm{dx}} ^ 2 = 12 x \left(x - 3\right) = 0$
$x = 0 , f \left(0\right) = 0 \text{ and } x = 3 , f \left(3\right) = - 81$