FINDING AVERAGE RATE OF CHANGE OF A FUNCTION
Definition of average rate of change :
The average rate of change between x = a and x = b is the slope of the secant line of the curve between the points x = a and x = b
For the following exercises, find the average rate of change of each function on the interval specified.
Problem 1 :
f(x) = x2 + 2 on [-1, 2]
Solution :
Given, f(x) = x2 + 2
a = -1 and b = 2
average rate of change = 1
Problem 2 :
f(x) = 4x2 - 7 on [1, b]
Solution :
Given, f(x) = 4x2 - 7
a = 1 and b = b
average rate of change = 4(b + 1)
Problem 3 :
g(x) = 2x2 - 9 on [4, b]
Solution :
Given, g(x) = 2x2 - 9
a = 4 and b = b
For each problem, find the average rate of change of the function over the given interval. You may use the provided graph to sketch the function.
Problem 4 :
f(x) = x2 - 2x + 1; [0, 1/3]
Solution :
Given, f(x) = x2 - 2x + 1
a = 0 and b = 1/3
Problem 5 :
Solution :
Problem 6 :
Solution :
Problem 7 :
f(x) = -x2 + 1; [-1, -3/4]
Solution :
Given, f(x) = -x2 + 1
a = -1 and b = -3/4
