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Worksheet: Average Value of a Function

Q1:

What is the average value of this function on the interval [ βˆ’ 5 , 4 ] ?

  • A15
  • B 1 9 9
  • C135
  • D 5 3
  • E βˆ’ 5 3

Q2:

What is the average value of this function on the interval [ βˆ’ 5 , 5 ] ?

  • A18
  • B 1 1 5
  • C180
  • D 9 5
  • E βˆ’ 9 5

Q3:

Find the average value of 𝑓 ( π‘₯ ) = √ 2 π‘₯ on the interval [ 0 , 2 ] .

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

Q4:

Find the average value of 𝑓 ( π‘₯ ) = √ 3 π‘₯ on the interval [ 0 , 3 ] .

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

Q5:

Determine the average value of 𝑓 ( π‘₯ ) = 3 π‘₯ βˆ’ 2 π‘₯ 2 on the interval [ βˆ’ 3 , 5 ] .

Q6:

Determine the average value of 𝑓 ( π‘₯ ) = 3 π‘₯ βˆ’ 8 π‘₯ 2 on the interval [ βˆ’ 1 , 3 ] .

Q7:

Find the average value of 𝑓 ( π‘₯ ) = π‘₯ ( π‘₯ βˆ’ 5 ) 2 3 2 on the interval [ βˆ’ 1 , 1 ] .

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

Q8:

Find the average value of 𝑓 ( π‘₯ ) = π‘₯ ( π‘₯ βˆ’ 3 ) 2 3 2 on the interval [ βˆ’ 2 , 1 ] .

  • A 9 2 2
  • B 3 2 2
  • C 3 5 4 8 4
  • D 1 2 2

Q9:

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

  1. 𝑓 β€² ( 1 )
  2. the average value of 𝑓 ( π‘₯ ) on 0 ≀ π‘₯ ≀ π‘Ž
  3. the average value of the rate of change of 𝑓 ( π‘₯ ) , for 0 ≀ π‘₯ ≀ π‘Ž
  4. ο„Έ 𝑓 ( π‘₯ ) π‘₯ π‘Ž 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 𝑓 ( 𝑒 ) = 𝑒 𝑒 l n on the interval [ 1 , 3 ] .

  • A l n 2 3 2
  • B 9 4
  • C l n 2 3
  • D l n 2 3 4

Q11:

Find the average value of 𝑓 ( 𝑒 ) = 𝑒 𝑒 l n on the interval [ 1 , 4 ] .

  • A l n 2 4 2
  • B 8 3
  • C 3 4 2 l n 2
  • D l n 2 4 6
  • E l n 2 4 3

Q12:

Find the average value of 𝑓 ( π‘₯ ) = 4 3 π‘₯ c o s on the interval  βˆ’ 5 πœ‹ 1 8 , 5 πœ‹ 1 8  .

  • A βˆ’ 1 2 5 πœ‹
  • B 4 3
  • C 2 0 πœ‹ 2 7
  • D 1 2 5 πœ‹
  • E0

Q13:

Find the average value of 𝑓 ( π‘₯ ) = 4 4 π‘₯ c o s on the interval  βˆ’ πœ‹ 2 4 , πœ‹ 2 4  .

  • A βˆ’ 1 2 πœ‹
  • B1
  • C πœ‹ 1 2
  • D 1 2 πœ‹
  • E0

Q14:

Find the average value of 𝑓 ( π‘₯ ) = ( 2 π‘₯ βˆ’ 5 ) 2 on the interval [ 1 , 4 ] .