Lesson 05.09 Analytical Applications of Differentiation Discussion-Based Assessment Assigned Problems 101234EBTBE 1. The gure above shows the graph of f', the derivative of the function f on the closed interval U s x s B. The graph of f ' has horizontal tangent lines at x = 2, x = 4, and x = E. The function fis twice differentiable. Part A: Find the xooordinate of each of the points of inection on the graph of 3'. Give a reason for your answer. Part B: At what value of 1: does f attain its absolute maximum value on the closed interval D s x 5 8'? Show the analysis that leads to your EHSWEI'. Part C: For what values of x is the graph of f concave upward? Justify your answer. 2. Let g be the function given by gm = x3 12x. Part A: Identify the relative extrema of g. Justify if your value is a local minimum, local maximum, or neither. Part B: On what interval(s) is the graph of g concave up? Justify your answer. 3. A twice-differentiable function fis defined for all real numbers x. The function f and its derivative have the properties and various values of x indicated in the table below. X 0 0