Question

find the average rate of change of the function on the specified interval.

$f(x)=-4x - 2$ on $4,8$

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here \(a = 4\), \(b=8\), and \(f(x)=-4x - 2\).

Step2: Calculate \(f(4)\) and \(f(8)\)

For \(x = 4\), \(f(4)=-4\times4-2=-16 - 2=-18\).
For \(x = 8\), \(f(8)=-4\times8-2=-32 - 2=-34\).

Step3: Substitute into the formula

\(\frac{f(8)-f(4)}{8 - 4}=\frac{-34-(-18)}{8 - 4}=\frac{-34 + 18}{4}=\frac{-16}{4}\)

Answer:

\(-4\)