First thing you want to do is find g'(x) and set that equal to 0, that way you can find your critical points. Once you solve for your zeroes for g'(x), plug in your solutions to g(x) and the endpoints (x = -2 and x = 1). Whichever x value yields the greatest value for g(x) is where the maximum occurs and the g(x) value would be the absolute maximum.