Question

Which formula below gives the average rate of change of the function z(x) = -6x + 2 + 3 on the interval -1 ≤ x ≤ 2 ?

Answer 1

The average rate of change is -6

Explanation:

The formula for average rate of change is

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

where

x₁=-1 and x₂=2

In this case we replace f(x) with z(x)

Substitute values of x₁ and x₂ in the formula given the function as

`z(x)=-6x+2+3\\z(x)=-6x+5\\\\\\=(z(x_2)-z(x_1))/(x_2-x_1) \\\\\\z(x_1)=z(-1)=-6*-1+5=6+5=11\\\\\\z(x_2)=z(2)=-6*2+5=-12+5=-7\\\\\\x_2-x_1=2--1=3\\\\Rateofchange=(-7-11)/(3) =(-18)/(3) =-6`