Finding the convex concave interval and inflection point of the curve y = x & # 178; - X & # 179

Finding the convex concave interval and inflection point of the curve y = x & # 178; - X & # 179

1] The definition domain of y = x & # 178; - X & # 179; is: R2] y '= 2x-3x & # 178; y' '= 2-6x. Solve the equation y' '= 0, then x = 1 / 3. In (- ∞, 1 / 3), y' '> 0, ■ (- ∞, 1 / 3) is the concave interval of the curve y = x & # 178; - X & # 179; similarly, [1 / 3, + ∞) is the convex interval of the curve y = x & # 178; - X & # 179; (1 / 3,2 / 27) curve