Question

How do you find the average rate of change of `f(x)=6x^2+1` over points (2, 25) and (3, 55)?

Answer 1

Average rate of change `= 30/1`

Explanation:

Given: `f(x) = 6x^2 + 1`. Find the average rate of change from `(2, 25)` and `(3, 55)`.

The average rate of change for a linear function is it's slope. When the function is not linear, the average rate of change is the slope between the two points.

Average rate of change `= (f(b) - f(a))/(b - a)`

Let `a = 2 => f(a) = 25; " "b = 3 => f(b) = 55`

Average rate of change `= (55 - 25)/(3 - 2) = 30/1`