posted by Roy .
Use the given derivative to find all critical points of 'f' and at each critical point determine whether a relative maximum, relative minimum, or neither occurs. Assume that 'f' is continuous everywhere.
f' (x) = (1-2x)/ ∛(x+3)
You have given us the derivative, and it is only zero when x = 1/2.
The derivatve becomes more negative when x>1/2, so x=1/2 is a relative maximum of f(x).