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Worksheet: Instantaneous Rate of Change

Q1:

Evaluate the rate of change of 𝑓 ( π‘₯ ) = 2 π‘₯ + 9 2 at π‘₯ = βˆ’ 3 .

Q2:

Evaluate the rate of change of 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 3 π‘₯ + 2 2 at π‘₯ = 5 .

Q3:

Find the rate of change of 5 π‘₯ βˆ’ 1 8 3 with respect to π‘₯ when π‘₯ = 2 .

Q4:

Evaluate the rate of change of 𝑓 ( π‘₯ ) = βˆ’ 9 4 π‘₯ βˆ’ 7 at π‘₯ = 4 .

  • A4
  • B βˆ’ 1
  • C βˆ’ 4 9
  • D 4 9

Q5:

Find the rate of change of 𝑓 ( π‘₯ ) = 4 π‘₯ βˆ’ π‘₯ βˆ’ 3 2 when π‘₯ = 1 and determine, to the nearest minute, the positive angle between the tangent at ( 1 , 0 ) and the positive π‘₯ -axis.

  • A 𝑓 ( 1 ) = 1 β€² , πœƒ = 4 5 0 β€² ∘
  • B 𝑓 ( 1 ) = 3 β€² , πœƒ = 7 1 3 4 β€² ∘
  • C 𝑓 ( 1 ) = 1 5 β€² , πœƒ = 8 6 1 1 β€² ∘
  • D 𝑓 ( 1 ) = 7 β€² , πœƒ = 8 1 5 2 β€² ∘

Q6:

Evaluate the rate of change of 𝑓 ( π‘₯ ) = √ 6 π‘₯ + 7 at π‘₯ = 3 .

  • A3
  • B 6 5
  • C5
  • D 3 5
  • E 1 1 0

Q7:

Determine the rate of change of the function 𝑓 ( π‘₯ ) = 5 9 π‘₯ at π‘₯ = √ 2 .

  • A βˆ’ 5 3 6
  • B 5 1 8
  • C 5 3 6
  • D βˆ’ 5 1 8

Q8:

If the function 𝑓 ( π‘₯ ) = 5 π‘₯ + 7 4 π‘₯ + 2 , determine its rate of change when π‘₯ = 2 .

  • A 5 9 5 0
  • B 1 7 1 0
  • C βˆ’ 9 5
  • D βˆ’ 9 5 0
  • E 1 8 2 8 9

Q9:

A length 𝑙 is initially 9 cm and increases at a rate of 3 cm/s. Write the length as a function of time, 𝑑 .

  • A 𝑙 = 3 𝑑
  • B 𝑙 = 9 𝑑
  • C 𝑙 = 3 + 9 𝑑
  • D 𝑙 = 9 + 3 𝑑

Q10:

Evaluate the rate of change of 𝑓 ( π‘₯ ) = 9 π‘₯ βˆ’ 4 7 π‘₯ at π‘₯ = 3 .

  • A 5 7 1 9
  • B9
  • C 5 7 1 2 1
  • D 5 7 1 6 3
  • E 4 6 3

Q11:

What is the rate of change for the function 𝑦 = 4 π‘₯ + 7 ?

Q12:

A circular disc preserves its shape as it shrinks. What is the rate of change of its area with respect to radius when the radius is 59 cm?

  • A 5 9 πœ‹ cm2/cm
  • B 1 1 8 πœ‹ cm2/cm
  • C βˆ’ 5 9 πœ‹ cm2/cm
  • D βˆ’ 1 1 8 πœ‹ cm2/cm

Q13:

Evaluate the rate of change of 𝑓 ( π‘₯ ) = 7 π‘₯ + 9 2 at π‘₯ = π‘₯ 1 .

  • A 7 β„Ž + 1 4 π‘₯ β„Ž 2 1
  • B 7 π‘₯ + 1 4 π‘₯ β„Ž + 7 β„Ž + 9 2 1 1 2
  • C 7 β„Ž + 1 4 π‘₯ 1
  • D 1 4 π‘₯ 1