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

z(2) - z(-1)
-------------
2 - (-1)

= (-6(2)^2 + 3 ) - ( -6(-1)^2 + 3
-----------------------------------------
3

= ( -21 - (-3)) / 3
= -18 / 3
= -6

Answer 2

Answer:
`(z(2)-z(1))/(2-(-1))`

Explanation:

The average rate of a function f(x) is interval [a,b] is given by :-

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

The given function:
`z(x)=-6x^2+3`

Interval : [-1,2]

Then using the above general formula , the average rate of change of the function z(x) = -6x^2 + 3 on the interval -1≤x≤2 is given by :-

`(z(2)-z(1))/(2-(-1))`