The answer to this question is 1. If we differentiate each piece, we get f'(x) = {2, -2 < x < 0 { -2x, x>0 The critical number is x = 0. We can also see that f(x) is decreasing on x>0. We check the end points and critical numbers for the absolute maximum. One end point at f(-2) = 2(-2) + 1 = -3 The critical number checked gives f(0) = -0^2 + 1 = 1 The absolute maximum value is 1.