Answer:
-3.98 (nearest hundredth)
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Given interval: -2 ≤ x ≤ 2
[tex]\implies a = -2[/tex]
[tex]\implies b = 2[/tex]
[tex]\implies f(a) = f(-2)=16[/tex]
[tex]\implies f(b) =f(2)= \dfrac{1}{16}[/tex]
Substituting the values into the equation:
[tex]\begin{aligned}\implies \textsf{rate of change} & =\dfrac{\frac{1}{16}-16}{2-(-2)}\\\\ & = \dfrac{-\frac{255}{16}}{4}\\\\ & = -\dfrac{255}{64}\\\\ & = -3.98\: \sf (nearest\:hundredth)\end{aligned}[/tex]
