Lesson Worksheet: Average and Instantaneous Rates of Change Mathematics • Higher Education

In this worksheet, we will practice finding the average rate of change of a function between two x-values and using limits to find the instantaneous rate of change.

Q1:

The average rate of change of a function 𝑓 between π‘₯ and π‘₯+β„Ž is 𝑓(π‘₯+β„Ž)βˆ’π‘“(π‘₯)β„Ž. Compute this quantity for 𝑓(π‘₯)=βˆ’4π‘₯βˆ’8 at π‘₯=βˆ’4, and for β„Ž=0.3.

Q2:

Let 𝑓(π‘₯)=βˆ’3π‘₯+7π‘₯βˆ’2. Compute the average rate of change function of 𝑓 as π‘₯ varies from 5 to 5.1.

Q3:

Evaluate the average rate of change for the function 𝑓(π‘₯)=βˆ’7π‘₯βˆ’3π‘₯+3 when π‘₯ changes from 1 to 1.5.

Q4:

Evaluate the average rate of change of 𝑓(π‘₯)=√2π‘₯βˆ’1 when π‘₯ varies from 5 to 5.62.

  • A23
  • B15
  • C1031
  • D165

Q5:

For the function 𝑓(π‘₯)=3π‘₯βˆ’14π‘₯+7, list the average rates of change of 𝑓 over the interval 3,3+110, where π‘˜=1,2,3,4, evaluated to 4 decimal places at most.

  • A3.6, 3.06, 3.006, 3.0006
  • B4.6, 4.06, 4.006, 4.0006
  • C3.3, 3.03, 3.003, 3.0003
  • D4.3, 4.03, 4.003, 4.0003
  • E3.4, 3.04, 3.004, 3.0004

Q6:

A farm’s production in kilograms 𝑦 as a function of the kilograms of insecticide π‘₯ is given by 𝑦=146βˆ’473π‘₯+8. Find the average rate of change in 𝑦 when π‘₯ varies from 13 to 17.

  • A347
  • B145
  • C359
  • D1259

Q7:

A triangular lamina with a base twice its height expands while maintaining its shape. Find the average rate of change in its area when its height changes from 14 cm to 23 cm.

Q8:

Determine the average rate of change for 𝑓(π‘₯)=6π‘₯βˆ’8 when π‘₯ changes from 8 to 8.4.

Q9:

Determine the average rate of change function 𝐴(β„Ž) for 𝑓(π‘₯)=6π‘₯βˆ’3 at π‘₯=1.

  • A𝐴(β„Ž)=6β„Ž+12β„ŽοŠ¨
  • B𝐴(β„Ž)=βˆ’6β„Ž+12
  • C𝐴(β„Ž)=βˆ’6β„Žβˆ’12
  • D𝐴(β„Ž)=6β„Ž+12

Q10:

Determine the average rate of change function 𝐴(β„Ž) for 𝑓(π‘₯)=4π‘₯+3π‘₯+2 at π‘₯=1.

  • A𝐴(β„Ž)=βˆ’4β„Žβˆ’11
  • B𝐴(β„Ž)=4β„Ž+11β„ŽοŠ¨
  • C𝐴(β„Ž)=βˆ’4β„Ž+11
  • D𝐴(β„Ž)=4β„Ž+11

This lesson includes 70 additional questions and 395 additional question variations for subscribers.

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