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
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                    3

=  ( -21 - (-3))  / 3
= -18 / 3
= -6

Answer 2

Answer: $\dfrac{z(2)-z(1)}{2-(-1)}$

Step-by-step explanation:

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

$\dfrac{f(b)-f(a)}{b-a}$

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 :-

$\dfrac{z(2)-z(1)}{2-(-1)}$