Average rate of change over an interval

Question 1

A ball is thrown upwards. Its height in metres after t seconds is h(t) = 19t − 5t². Find its average speed upwards (rate of change of height, in m/s) from t = 0 to t = 1. A negative answer means it is coming down.

Answer 

Question 2

f(x) = −x² + 2x − 3. Find the average rate of change of f between x = −3 and x = 1.

Answer 

Question 3

x: 0, 1, 2, 3, 4 f(x): −3, −2, 1, 6, 13 Find the average rate of change of f from x = 0 to x = 4.

Answer (as a fraction)

Question 4

A ball is thrown upwards. Its height in metres after t seconds is h(t) = 28t − 5t². Find its average speed upwards (rate of change of height, in m/s) from t = 0 to t = 1. A negative answer means it is coming down.

Answer 

Question 5

f(x) = 2x² + 5x − 6. Find the average rate of change of f between x = 0 and x = 4.

Answer 

Question 6

x: 0, 1, 2, 3, 4 f(x): 3, 3, 9, 21, 39 Find the average rate of change of f from x = 0 to x = 4.

Answer (as a fraction)

Question 7

A ball is thrown upwards. Its height in metres after t seconds is h(t) = 27t − 5t². Find its average speed upwards (rate of change of height, in m/s) from t = 1 to t = 3. A negative answer means it is coming down.

Answer 

Question 8

f(x) = 2x² − 4x + 4. Find the average rate of change of f between x = −2 and x = −1.

Answer 

Question 9

x: 0, 1, 2, 3, 4 f(x): −4, −4, 2, 14, 32 Find the average rate of change of f from x = 0 to x = 2.

Answer (as a fraction)

Question 10

A ball is thrown upwards. Its height in metres after t seconds is h(t) = 23t − 5t². Find its average speed upwards (rate of change of height, in m/s) from t = 0 to t = 1. A negative answer means it is coming down.

Answer 

Question 11

f(x) = x² + 4x. Find the average rate of change of f between x = −1 and x = 0.

Answer 

Question 12

x: 0, 1, 2, 3, 4 f(x): 1, 4, 11, 22, 37 Find the average rate of change of f from x = 1 to x = 3.

Answer (as a fraction)

Question 13

A ball is thrown upwards. Its height in metres after t seconds is h(t) = 26t − 5t². Find its average speed upwards (rate of change of height, in m/s) from t = 2 to t = 3. A negative answer means it is coming down.

Answer 

Question 14

f(x) = −2x² + 4x + 4. Find the average rate of change of f between x = −3 and x = −1.

Answer 

Question 15

x: 0, 1, 2, 3, 4 f(x): 4, 8, 16, 28, 44 Find the average rate of change of f from x = 1 to x = 4.

Answer (as a fraction)

Question 16

A ball is thrown upwards. Its height in metres after t seconds is h(t) = 21t − 5t². Find its average speed upwards (rate of change of height, in m/s) from t = 0 to t = 1. A negative answer means it is coming down.

Answer