The critical point c is the x where G' is 0. Once you've got that point, evaluate G' for some a < c and some b > c, where a and b are close to c (preferably 1 unit away). If G'(a) - G'(b) > 0 then G'(c) is a relative maximum and if G'(a) - G'(b) < 0 then G'(c) is a relative minimum. Generally, you are given an interval in extremum problems.

Source:

Finding Relative Extrema — MATH201 (TC3, Brown)

Calculus (Johnston and Mathews)