1. Determine f"(x) given fo) = x6 + x5 + 7x 8 2. Given f(x) = 4-x + S,g(x) = 5:):2 3x + 8, determine the derivatives of the following functions. Simplify your solutions. a) (f X g)(x) hi (1' + 5000 c) (fa y)(x) dl (g a f)(x) 3. A piece of sheet metal, 50cm by 20cm is to be used to make a rectangular box with an open top. Determine the dimensions that will give the box with the largest volume. Curve Sketching 1. Identify the type of point for each of the following and then sketch a graph of what such a function could look like 2. Determine the points of inflection and the intervals of concavity ofthe function f(x) = 3x5 15x4 102:3 + 903:2 + 42x 23 3. Graph the function f(x) = 3x4 4x3 24-):2 + 48x 17. Label 3: and y intercepts (when possible}, any asymptotes, local maxima, local minima, and points of inflection. 4. Graph the function f(x) = 1:23:6- local maxima, local minima, and points of inflection. Label 1: and y intercepts {when possible), any asymptotes