( 2 5), 3 : Let be the function defined by () = { 5 2, >3 The function is twice differentiable on the closed interval [2, 10] and satisfies (6) = 4. The graph of , the derivative of , is shown in the figure above. The graph of has horizontal tangent lines at = 2, = 5, = 8, and = 9. The areas of the regions between the graph of and the axis are labeled in the figure. (a) Show that is continuous at = 3. (b) Find the absolute maximum value of on the interval [2,10]. Justify your answer. 3 (c) For 3, the function is defined by () = 3 4 () 4 3 2()+5 . It is known that lim () 3 can be evaluated using L Hospital s Rule. Find (3) and evaluate lim (). 3 Created by Bryan Passwater bryanpasswater1@gmail.com ( 2 5), 3 : Let be the function defined by () = { 5 2, >3 The function is twice differentiable on the closed interval [2, 10] and satisfies (6) = 4. The graph of , the derivative of , is shown in the figure above. The graph of has horizontal tangent lines at = 2, = 5, = 8, and = 9. The areas of the regions between the graph of and the axis are labeled in the figure. (d) Let = () be a function such that 1 2 = (2) (3 1) where > . Find and 3 2 use this expression to determine if the graph of () is concave up or down at (1) = 2. (e) Consider the function = () from part (d). For 1