AVERAGE RATE OF CHANGE OF A FUNCTION

Problems 1-9 : Find the average rate of change of the function f(x) over the given interval.

Problem 1 :

f(x) = x² - x + 1

[0, 3]

Solution :

The average rate of change of f(x) in [0, 3] :

= 2

Problem 2 :

[-3, -2]

Solution :

The average rate of change of f(x) in [-3, -2] :

Problem 3 :

[9, 3]

Solution :

The average rate of change of f(x) in [9, 3] :

Problem 4 :

f(x) = x² + 2

[-2, -1.5]

Solution :

The average rate of change of f(x) in [-2, -1.5] :

= -3.5

Problem 5 :

Solution :

The average rate of change of f(x) in [1, 2] :

Problem 6 :

f(x) = sin x

Solution :

Problem 7 :

f(x) = cos x

Solution :

Problem 8 :

f(x) = tan x

Solution :

Problem 9 :

f(x) = ln(x)

[e, e²]

Solution :

The average rate of change of f(x) in [e, e²] :

Problem 10 :

In the graph shown below, find the average rate of change of the curve from x = 4 to x = 9.

Solution :

The average rate of change from x = 4 to x = 9 :

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