Understanding the graph of a function is essential for analyzing its behavior and extracting valuable information. The graph of a function F can provide insights into its domain, range, extrema, and other characteristics. However, sometimes we are given not the function F directly but its derivative F’. In such cases, we need to find a way to construct the graph of F from the information provided by F’. This process is known as finding the antiderivative of F’ or integrating F’.
Finding the graph of F given F’ involves several steps. First, we need to integrate F’ with respect to x to obtain F(x). Integration is the inverse operation of differentiation, and it allows us to recover the original function from its derivative. Once we have F(x), we can plot its graph using the standard techniques of graphing functions.
