The question is usually asked the other way around. IOW, If you have a relative maximum (or minimum), how can you tell if it is ALSO an absolute maximum (minimum)?Neen87 said:Homework Statement
I do not have a specific homework problem, but could someone please clarify this for me?
QUESTION: When you have an absolute maxima (or minima), how can you tell if it is ALSO a relative maxima (or minima)?
I understand how to find absolute extrema on a closed interval, and how to find critical values of a function by setting f'(x) = 0 and when f'(x) is undefined.
Thank you!
Tina
Absolute maxima and minima are the highest and lowest values of a function over its entire domain, while relative maxima and minima are the highest and lowest values within a specific interval of the function.
Absolute maxima and minima are identified by finding the highest and lowest points on the graph, respectively. Relative maxima and minima are identified by finding where the slope of the graph changes from positive to negative (for maxima) or negative to positive (for minima).
Yes, a function can have multiple absolute or relative maxima or minima. This can occur when there are multiple peaks or valleys in the graph of the function.
Absolute and relative maxima and minima are used in optimization problems, such as finding the maximum profit or minimum cost in business or engineering scenarios. They can also be used in data analysis to identify the highest and lowest values in a dataset.
Yes, there is a relationship between absolute and relative maxima and minima. Relative maxima and minima are always included within the range of absolute maxima and minima. In other words, the absolute maxima and minima are the highest or lowest values that the function can attain, while the relative maxima and minima are the highest or lowest values within a smaller interval of the function.