Worksheet: The Average Value of a Function

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In this worksheet, we will practice calculating the average value of a function, also known as the mean, for continuous functions over intervals.

Q1:

The average value of on the interval is 0. Find all possible values of .

  • A or
  • B or
  • C or
  • D or

Q2:

Find all such that equals the average value of over the interval .

  • A ,
  • B5,
  • C ,
  • D ,

Q3:

Find the average value of on the interval .

  • A
  • B
  • C
  • D
  • E

Q4:

Find the average value of on the interval .

  • A
  • B
  • C
  • D
  • E

Q5:

What is the average value of this function on the interval ?

  • A15
  • B
  • C135
  • D
  • E

Q6:

Find the average value of 𝑓 ( 𝑥 ) = √ 2 𝑥 on the interval [ 0 , 2 ] .

  • A 8 3
  • B 2
  • C 1 6 3
  • D 4 3
  • E 1

Q7:

Determine the average value of on the interval .

Q8:

Find the average value of 𝑓 ( 𝑥 ) = 𝑥 ( 𝑥 − 5 ) 2 3 2 on the interval [ − 1 , 1 ] .

  • A 1 3 6
  • B 1 2 4
  • C 1 1 8
  • D 1 7 2
  • E 5 2 8 8

Q9:

Using the figure, arrange the following from least to greatest:

  1. 𝑓 ′ ( 1 )
  2. the average value of 𝑓 ( 𝑥 ) on 0 ≤ 𝑥 ≤ 𝑎
  3. the average value of the rate of change of 𝑓 ( 𝑥 ) , for 0 ≤ 𝑥 ≤ 𝑎
  4. 𝑓 ( 𝑥 ) 𝑥 𝑎 0 d
  • AB, D, C, A
  • BA, D, C, B
  • CC, D, B, A
  • DA, C, B, D
  • EA, C, D, B

Q10:

Find the average value of on the interval .

  • A
  • B
  • C
  • D

Q11:

Find the average value of on the interval .

  • A
  • B
  • C
  • D
  • E0

Q12:

Find the average value of on the interval .

Q13:

Find all such that equals the average value of over the interval .

  • A
  • B
  • C
  • D
  • E

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