What is the average rate of change of the function over the interval x = 0 to x = 5?
f(x) = 42x + 1

Solution:

Given f(x) = 42x + 1; interval (0, 5)

To find the average rate of change, we divide the change in y(output) by the change in x(input).

Average rate of change = {f(b) - f(a)}/(b - a) ; (a, b) =(0, 5)

f(b)= f(5) = 42x + 1 = 42(5) +1 = 211

f(a) = f(0) = 42x + 1 = 42(0) +1 =1

Rate of change = (211 -1)/(5 - 0)

= 210/5

= 42

What is the average rate of change of the function over the interval x = 0 to x = 5?
f(x) = 42x + 1

Summary:

The average rate of change of the function f(x) = 42x + 1over the interval x = 0 to x = 5 is 42.