Question

If
f (x) = x^2 - 4
what is the average rate of change from x = 3 to x = 5?

Answer 1

The average rate of change is 8

Explanation:

Mathematically, we have the average rate of change over a given interval as;

f(b) - f(a)/b-a

Where the interval is [a,b]

With respect to this question, a = 3 and b = 5

f(a) = f(3) = 3^2 - 4 = 9-4 = 5

f(b) = f(5) = 5^2 - 4 = 25-4 = 21

Thus, the average rate of change over the intervals will be;

(21-5)/(5-3) = 16/2 = 8