Average rate of change of the function: [tex]-\sqrt{3}[/tex]
Step-by-step explanation:
The average rate of change of a function f(x) can be calculated as:
[tex]r=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
where:
[tex]x_1, x_2[/tex] are the x-values of the interval taken into account to evaluate the rate of change of the function
[tex]f(x_1),f(x_2)[/tex] are the values of the function at those points
In this problem, we have:
[tex]x_1=8\\x_2=64[/tex]
The function is [tex]f(x)=-x\sqrt{3}[/tex], so
[tex]f(x_1)=f(8)=-8\sqrt{3}\\f(x_2)=f(64)=-64\sqrt{3}[/tex]
So, the average rate of change in this interval is:
[tex]r=\frac{-64\sqrt{3}-(-8\sqrt{3})}{64-8}=\frac{-56\sqrt{3}}{56}=-\sqrt{3}[/tex]
Learn more about rates of change:
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