1. The problem statement, all variables and given/known data x^4 - 6x^3 + 12x^2 - 8x a) Find all points of infliction of this function b) Sketch the function and identify all convex and concave portions of the curve c) Find the equations of the slopes at each point of infliction 2. Relevant equations x^4 - 6x^3 + 12x^2 - 8x 3. The attempt at a solution Hello, What I attempted to do was to do the second derivative of the function (as I dont need to determine min/max there is no need to bother with the first derivative right, i.e. finding the points at which the slope is 0?). After finding the second derivative I just solve it such as that y''=0 for a given x. a) y' = 4x^3 - 18x^2 + 24x - 8 y'' = 12x^2 - 36x + 24 Solving X such as that y'' = 0 (infliction points): [-(-36) +/- sqrt(-36^2 - (4*12*24)] / 2*12 Which yields: (36+/- 12) / 24 ----> x = 2, x = 1 So the infliction points are x=2 and x=1. b) I think I got this one right as it's just a matter of plugging in different values for X and plot it in a graph. c) This is the one I cant figure out how to do. I am supposed to find the equations of the slopes at each point of infliction, but I dont quite understand the question. Do I just plug in the x value in the original function? Ex. x = 1 ---> Equation at infliction pt: 1-6+12-8 = -1 ?? I would really appriciate some guidance as to how I am supposed to do c). Thanks!