Find the monotone interval and extremum of y = x3-6x2 + 9x-5

Find the monotone interval and extremum of y = x3-6x2 + 9x-5

∵ y = x3-6x2 + 9x-5, ∵ y ′ = 3x2-12x + 9 = 3 (x2-4x + 3) = 3 (x-3) (x-1) let y ′ < 0, the solution is 1 < x < 3; let y ′ > 0, the solution is x > 3 or x < 1; the monotone increasing interval of function y = x3-6x2 + 9x-5 is (- ∞, 1) or (3, + ∞), and the monotone decreasing interval of function y = x3-6x2 + 9x-5 is (1, 3); when x = 1, the maximum is - 1, and when x = 3, the minimum is obtained. ∵ f (x) maximum =F (1) = - 1; & nbsp; f (x) minimum = f (3) = - 5