Question

find the average rate of change of ( f(x)=\frac{-16}{x} ) over the interval ( -3,2 ).
write your answer as an integer, fraction, or decimal rounded to the nearest tenth.
simplify any fractions.

Explanation:

Step1: Recall the formula for average rate of change

The formula for 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, \(a=-3\), \(b = 2\), and \(f(x)=\frac{-15}{x}\).

Step2: Calculate \(f(a)\) and \(f(b)\)

When \(x=-3\), \(f(-3)=\frac{-15}{-3}=5\). When \(x = 2\), \(f(2)=\frac{-15}{2}=-7.5\).

Step3: Substitute into the formula

\(\frac{f(2)-f(-3)}{2-(-3)}=\frac{-7.5 - 5}{2 + 3}=\frac{-12.5}{5}=-2.5\)

Answer:

\(-2.5\)