y = x3 + x2 - x + 1 dydx = d(x3)dx + d(x2)dx - d(x)dx + d(1)dx dydx = 3x2 + 2x - 1 = 0 dydx = 3x2 + 2x - 1 At the maximum point dydx = 0 3x2 + 2x - 1 = 0 (3x2 + 3x) - (x - 1) = 0 3x(x + 1) -1(x + 1) = 0 (3x - 1)(x + 1) = 0 therefore x = 13 or -1 For the maximum point d2ydx2 < 0 d2ydx2 6x + 2 when x = 13 dx2dx2 = 6(13) + 2 = 2 + 2 = 4 d2ydx2 > o which is the minimum point when x = -1 d2ydx2 = 6(-1) + 2 = -6 + 2 = -4 -4 < 0 therefore, d2ydx2 < 0 the minimum point is 1/3
