I have a test tomorrow and I'm not sure how to solve this. I need to find: inflection points, where f(x) is increasing, concave up, and local min/max points. [tex]f(x) = 3x^4 - 4x^3[/tex] [tex]f'(x) = 12x^3 - 12x^2[/tex] [tex]f'(x) = 12x(x-1)[/tex] So I get: x = 0 and x = 1 These are my critical points right? Are these the same as inflection points? anyway: [tex]x-1 > 0 [/tex] so, I get f(x) is increasing when x>1. Or (1, Infinity) Now I find concavity: [tex] f''(x) = 36x^2 - 24x [/tex] [tex] 6x(6x-4)[/tex] [tex] 6x = 0 , x = 0[/tex]and [tex] 6x-4 = 0 , x = 2/3[/tex] So I get: f(x) is concave up from (-infinity, 0)u(2/3, infinity) So I figured out about half of the problem. I guess what I really need help with is how to find the inflection points, and how those are different from the critical points. And also how to find the local min/max values. Any help is really appreciated.