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.