Question

t g(t) -5 6 -4 4 -3 2 -2 1 -1 -1 0 -2 1 -3 2 1 3 3 4 6 5 9 what is the average rate of change of g over the interval -4 ≤ t ≤ 1? give an exact number. related content worked example: average rate of change from graph

Explanation:

Step1: Find the values of \(g(t)\) at the endpoints

When \(t = - 4\), \(g(-4)=4\). When \(t = 1\), \(g(1)=-3\).

Step2: Use the average rate of change formula

The formula for the average rate of change of a function \(y = g(t)\) over the interval \([a,b]\) is \(\frac{g(b)-g(a)}{b - a}\). Here, \(a=-4\), \(b = 1\). So, \(\frac{g(1)-g(-4)}{1-(-4)}=\frac{-3 - 4}{1 + 4}\).

Step3: Calculate the result

\(\frac{-3-4}{1 + 4}=\frac{-7}{5}=-1.4\)

Answer:

\(-1.4\)