Question

How do you find the average rate of change of `(x) = 3x^2 + 1` over [1,4]?

Answer 1

15

Explanation:

the average rate of change is the slope

slope = `(Deltay)/(Deltax)`

= `(f(4) - f(1)) / (x_2 -x_1`

f(4) = `3(4)^2 + 1 = 48 + 1 = 49`
f(1) = `3(1)^2 + 1 = 3 + 1 =4`

so slope = `(49 - 4) /(4 - 1)` = `45/3` = 15