The average rate of change of a function over a specific interval can be found using the formula:
Average Rate of Change = (f(b) – f(a)) / (b – a)
In this case, we have the function f(x) = 42x + 1, and we are interested in the interval [0, 5]. Here, a = 0 and b = 5.
First, we need to calculate f(0) and f(5):
- f(0) = 42(0) + 1 = 1
- f(5) = 42(5) + 1 = 210 + 1 = 211
Now, we can apply the values we found into the average rate of change formula:
Average Rate of Change = (f(5) – f(0)) / (5 – 0)
Average Rate of Change = (211 – 1) / (5 – 0) = 210 / 5 = 42
Therefore, the average rate of change of the function f(x) = 42x + 1 over the interval from x = 0 to x = 5 is 42.