The following problems illustrate detailed graphing of functions of one variable using the first and second derivatives.
Problems range in difficulty from average to challenging.
If you are going to try these problems before looking at the solutions, you can avoid common mistakes by carefully labeling critical points, intercepts, and inflection points. In addition, it is important to label the distinct sign charts for the first and second derivatives in order to avoid unnecessary confusion of the following well-known facts and definitions. For example, mark those x -values where division by zero occurs in f ' . Above these x -values and the sign chart draw a dotted vertical line to indicate that the value of f ' does not exist at this point. These designated x -values establish intervals along the sign chart.