Absolute values? Consider the function f(x) = |x?2|+|x?3| on [?4, 4]. Graph f, identify the critical points, and give the coordinates of the local and absolute extreme values.
Solution Step 1 In this problem we have to find the critical points of the function f(x) = |x2|+|x3| and also we have to identify absolute maximum and absolute minimum. First let us see the definitions of critical point, absolute maximum,absolute minimum. Critical point: An interior point cof the domain of a function f at which f (c) = 0or f(c)fails to exist is called a critical point of f Absolute maximum: The highest point over the entire domain of a function or relation is the absolute maximum. Absolute minimum: The lowest point over the entire domain of a function or relation is the absolute minimum. Step 2 Let us use Ti-83 calculator to draw the graph of the given function. The steps involved in Ti-83 calculator are as follows: Step1: Press Y= and enter the above function The screenshot of this step in Ti-83 calculator is shown below Step 3 Step2: Press WINDOW button to adjust the window and set the range of the axis as [5,10]×[10,12] The screenshot of window adjustment is shown below