Help me find the zeroes of this function: f(x)=1/2x^3-2x

Try factoring it.

f(x) = (1/2)x^3 - 2x
= x[(x^2/2) -2)
= (x/2)(x^2-4)
= (x/2)(x+2)(x-2)
is zero when x = -2, 0 or 2.