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Extrema of Functions Worksheet

This worksheet focuses on identifying and understanding the extrema (maximum and minimum values) of functions, including absolute and relative extrema.

Grade 9 Math CalculusExtrema
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Includes

2 Short AnswerMultiple ChoiceFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSF.IF.C.7.ECCSS.MATH.CONTENT.HSF.BF.B.3

Topics

MathCalculusExtremaFunctionsMaximumMinimum
7 sections · Free to use · Printable
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Extrema of Functions

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Date:

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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)
a

(2, -1)

b

(4, 3)

c

Neither a nor b

d

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.

T

True

F

False

7. Every continuous function on an open interval must have an absolute maximum and minimum.

T

True

F

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.