The absolute maximum of a function is the highest value that the function reaches over its entire domain. Similarly, the absolute minimum is the lowest value that the function reaches over its entire domain.
To find the absolute maximum/minimum of a function, you need to take the derivative of the function and set it equal to zero. Then, solve for the critical points of the function and evaluate the function at these points to determine the absolute maximum/minimum.
The relative maximum/minimum of a function refers to the highest or lowest value of the function within a specific interval. The absolute maximum/minimum, on the other hand, refers to the highest or lowest value of the function over the entire domain.
No, a function can only have one absolute maximum and one absolute minimum. This is because the absolute maximum/minimum refers to the highest/lowest value of the function over its entire domain.
Finding the absolute maximum/minimum of a function can be useful in many real-world applications, such as optimizing production processes, maximizing profits, and minimizing costs. It can also help in determining the maximum or minimum values of physical quantities, such as temperature or pressure, in a given system.