To calculate the average rate of change of a function over an interval, we use the formula:
Average Rate of Change = (f(b) - f(a)) / (b - a)
For the function f(x):
f(0) = (3/2 * 0) + 2 = 2
f(3) = (3/2 * 3) + 2 = 9/2 + 2 = 13/2
Average Rate of Change of f(x) over [0, 3] = (f(3) - f(0)) / (3 - 0) = (13/2 - 2) / 3 = (13/2 - 4/2) / 3 = 9/6 = 3/2 = 1.5
For the function g(x):
g(0) = -4
g(3) = -10
Average Rate of Change of g(x) over [0, 3] = (g(3) - g(0)) / (3 - 0) = (-10 - (-4)) / 3 = (-10 + 4) / 3 = -6 / 3 = -2
Therefore, the average rate of change of f(x) over the interval [0, 3] is 1.5 and the average rate of change of g(x) over the same interval is -2.
Comparing the rates, we find that the magnitude of the rate of change of f(x) is greater than the magnitude of the rate of change of g(x). Therefore, f(x) is changing at a faster rate than g(x).
A function is represented by f(x)=3/2x+2 . Another function, g(x) , has the following table of values:
X -1 0 1 2 3
g(x) 0 -4 -3 -6 -10
What is the average rate of change of f(x) and g(x) over the interval [0, 3] , and which function is changing at a faster rate?
1 answer