Lesson 05.11 Analytical Applications of Differentiation Discussion-Based Assessment Assigned Problems 1. The figure above shows the graph of f', the derivative of the function f on the closed interval 0 s x s 8. The graph of f' has horizontal tangent lines at x = 2, x = 4, and x = 6. The function f is twice differentiable. Part A: Find the x-coordinate of each of the points of inflection on the graph of f. Give a reason for your answer. Part B: At what value of x does f attain its absolute maximum value on the closed interval 0 s x S 8? Show the analysis that leads to your answer. 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 g(x) = 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 f is 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. 0 0