find the x coordinates of all relative points of f(x)=1/2x^4-2/3x^3-6x^2-100
using brackets I read yours as
f(x) = (1/2)x^4 - (2/3)x^2 - 100
f ' (x) = 2x^3 - (4/3)x
= 0 for max/min
2x^3 - (4/3)x = 0
6x^3 - 4x = 0
2x(x-2) = 0
x = 0 or x = 2
take it from there