Extrema of Functions Worksheet
This worksheet focuses on identifying and understanding the extrema (maximum and minimum values) of functions, including absolute and relative extrema.
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Extrema of Functions
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Read each question carefully and answer to the best of your ability. Show all work where applicable.
1. Define what an 'absolute maximum' of a function means in your own words.
2. How does a 'relative minimum' differ from an 'absolute minimum'?
3. The graph of a function is shown below. At which point does the function have a relative maximum?
(2, -1)
(4, 3)
Neither a nor b
Both a and b
4. A function must be on a closed interval to guarantee the existence of both an absolute maximum and an absolute minimum.
5. The points where a function changes from increasing to decreasing, or vice versa, are called points.
6. A function can have more than one absolute maximum value.
True
False
7. Every continuous function on an open interval must have an absolute maximum and minimum.
True
False
8. Consider the function f(x) = x^2 - 4x + 3 on the interval [0, 5]. Find the absolute maximum and minimum values of the function on this interval. Show your work.