Question

How do you find the average rate of change of `f(t) = 1.1t^2 - 2.5t + 1.5` over the interval [3,5]?

Answer 1

6.3

Explanation:

The average rate of change of a function over an interval `[a, b]` is the same as the slope of the line going through the points `(a, f(a))` and `(b, f(b))`. As an expression, this is `\frac{f(b)-f(a)}{b-a}`.

In this case, the line goes through (3, 3.9) and (5, 16.5). Thus, the average rate of change of `f(x)` over the interval `[3, 5]` is equal to `\frac{16.5-3.9}{5-3}=6.3`