The formula to find the average rate of change of the function f(x) in the interval [x_{1}, x_{2}] :
Problems 1-9 : Find the average rate of change of the function f(x) over the given interval.
Problem 1 :
f(x) = x^{2} - 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) = x^{2} + 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, e^{2}]
Solution :
The average rate of change of f(x) in [e, e^{2}] :
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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