Analysis of a Family of Curves
This Demonstration calculates the information needed for a careful sketch of each of the graphs of the functions in the family . In addition, the area under the curve and the volumes of revolution are calculated.
The presented program analyzes and visualizes a one-parameter family of functions. You can replace the function in the program.
Extreme points and inflection points are highlighted in the graph on the left. A change of the interval limits and will only result in a change to the area and volume calculations.
For the calculation of the area under the curve, choose the interval so that all function values in this interval are positive or negative (in the latter case, the value of the integral is the negative of the area).