Critical Points from Graph of Derivative Function

In this example problem, we go through several examples where the graph of the derivative's graph f'(x) is given and we are asked to determine how many critical points the original function f(x) will have. To do so, we know that a function will only have critical values or critical numbers that correspond with critical points when the derivative is either undefined or equal to zero. Because each of our derivative graphs are polynomial functions, they are not undefined anywhere so we do not worry about that situation. To determine when the derivative will equal zero is the same as looking for when it has x-intercepts. By counting the number of x-intercepts on each derivative graph, we find the number of critical points that will be on the original function's graph.