meeklobraca said:Okay I've found the derivative of t + cot (t/2) to be
1 - csc^2(t/2) * 1/2
The absolute maximum is the highest point on a graph or function, while the absolute minimum is the lowest point. These points are also known as global maximum and global minimum, as they represent the overall highest and lowest values of the function.
To find the absolute maximum and minimum, you must first take the derivative of the function and set it equal to zero. Then, solve for the critical points by finding the roots of the derivative. Next, evaluate the function at each critical point and the endpoints of the given interval. The largest and smallest values obtained from these evaluations will be the absolute maximum and minimum, respectively.
Yes, it is possible for a function to have multiple absolute maximum or minimum points. This occurs when the function has a flat region, or plateau, where the function has the same value for a certain interval. In this case, all points on the plateau will be considered absolute maximum or minimum points.
Finding the absolute maximum and minimum points of a function can provide valuable information about the behavior and characteristics of the function. It can help determine the range of the function, the location of critical points, and the overall shape of the graph. This information is useful in various applications, such as optimization problems in mathematics and science.
While there are no shortcuts for finding the absolute maximum and minimum, there are some techniques that can make the process easier. For example, using a graphing calculator or software can help visualize the function and identify the maximum and minimum points. Also, understanding the behavior of basic functions, such as linear and quadratic functions, can provide insight into the general shape and location of the maximum and minimum points.