Extrema of Piecewise[{{-5x-19, -6 <= x < -5}, {11, x=-5}, {6, -5 < x <= -2}, {x^2+2, -2 <= x <= 3}, {-8x/3+19, 3 <= x <6}, {5x-32, 6<=x<=7 }}] for -6<=x<=7