What are the points of inflection, if any, of f(x) = x^4/2 - 2x^3 + 5 ?

Points of inflection are $\left(0 , 5\right)$ and $\left(2 , - 3\right)$
Determine the 2nd derivative $f ' ' \left(x\right)$ then equate to zero.
the values of $x$ are 0 and 2.
go back to the original function $f \left(x\right) = {x}^{4} / 2 - 2 {x}^{3} + 5$ to solve for the y values.